Calculated t-value (-3) is less than the critical t-value (-1.69), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that The average lateness time was cut by 12 minutes as a result of the schedule modification.
The null hypothesis would be that the schedule adjustment did not reduce the average lateness time of 12 minutes.
[tex]H0:[/tex][tex]\mu = 12[/tex]
The alternative hypothesis would be that the schedule adjustment did reduce the average lateness time of 12 minutes.
[tex]Ha:[/tex] [tex]\mu < 12[/tex]
Here, we are testing whether the population mean arrival time is less than 12 minutes, based on a sample of 36 runs that had an average of 8 minutes late. We can use a one-sample t-test to test this hypothesis, with the following test statistic:
[tex]t = (\bar x - \mu) / (s / \sqrt{n} )[/tex]
where[tex]\bar x[/tex] is the sample mean (8 minutes),[tex]\mu[/tex] is the population mean (12 minutes), s is the population standard deviation (12 minutes), and n is the sample size (36 runs).
Using these values, we get:
[tex]t = (8 - 12) / (12 / \sqrt{(36)} ) = -3[/tex]
The degrees of freedom for this test are n - 1 = 35. Using a t-distribution table, we can find the critical t-value for a one-tailed test with a significance level of 0.05 and 35 degrees of freedom to be approximately -1.69.
Since our calculated t-value (-3) is less than the critical t-value (-1.69), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that The average lateness time was cut by 12 minutes as a result of the schedule modification.
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Use the equation y = 7x to complete the table. What are the missing values of
y?
O A. When x = 2, y = 16.
When x = 4, y = 30.
O B. When x = 2, y = 14.
When x = 4, y = 28.
C. When x = 2, y = 8.
When x = 4, y = 22
D. When x = 2, y = 12.
When x = 4, y = 24.
Using the equation y = 7x , we can compute that when x = 2, y = 14 and when x = 4 , y = 28. So, correct option is B.
The equation y = 7x relates the variables y and x, where y is a function of x. To compute the value of y for a given value of x, we simply substitute that value of x into the equation and solve for y.
When x = 2, we can substitute this value into the equation:
y = 7(2) = 14
Therefore, when x = 2, y = 14.
Similarly, when x = 4, we can substitute this value into the equation:
y = 7(4) = 28
Therefore, when x = 4, y = 28.
So, the correct option is B: When x = 2, y = 14 and when x = 4, y = 28.
In summary, to compute the value of y for a given value of x using an equation, we substitute that value of x into the equation and solve for y. In this case, when x = 2, y = 14, and when x = 4, y = 28, according to the given equation y = 7x.
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Seven liters of cran-strawberry juice is added to an unknown amount of cran-orange juice to make a fruit punch. The cran-strawberry juice contains 65% cranberry juice. The cran-orange juice contains 50% cranberry juice. The fruit punch contains 60% cranberry juice. How much cran-orange juice does the fruit punch contain?
50%
The cran-orange juice contains 50% cranberry juice. The juice is 100% juice. Subtract 50% cranberry juice from 100% cran-orange juice and that leaves you with 50% orange juice.
Solve 5(p−3q)<12 for q
The value of q in the question is q>-12/15
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions
The given inequality is 5(p−3q)<12
Opening the bracket we have
5p - 15q < 12
The solution can only be gotten if we assume p = 0
the substitute p=0 in the inequality to have
-15q < 12
dividing both sides by -15 to have
-15q/-15 < 12/-15
therefore q > 12/-15
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Find the missing length of the triangle. 7.2 feet, 9.6 feet, and c
By using pythagorean theorem, the length of the missing side is 12 feet.
What is the Pythagorean theorem?
Pythagoras' theorem is a fundamental principle in geometry that relates to the three sides of a right-angled triangle. It states that:
"In a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides."
In mathematical terms, if a, b, and c are the lengths of the sides of a right-angled triangle, where c is the hypotenuse, then the theorem can be written as:
[tex]c^2 = a^2 + b^2[/tex]
We can use the Pythagorean theorem to determine the length of the missing side if we know that the given sides form a right triangle.
In this case, we have two sides of the triangle given: 7.2 feet and 9.6 feet. Let's assume that c is the length of the hypotenuse.
If the triangle is a right triangle, then we can use the Pythagorean theorem to solve for c:
[tex]c^2 = 7.2^2 + 9.6^2[/tex]
[tex]c^2 = 51.84 + 92.16[/tex]
[tex]c^2 = 144[/tex]
[tex]c = \sqrt{144}[/tex]
c = 12 feet
Therefore, if the triangle is a right triangle, then the length of the missing side is 12 feet.
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Weights of adult males.
The weights of adult individuals in a certain country are normally distributed with a population mean of μ=172 pounds and a population standard deviation of σ=29 pounds. Suppose n=36 individuals are sampled.
1)
What is the mean of the sampling distribution of the means?
The sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.
In the context of sampling distribution of the means, the standard deviation represents the degree of spread or variation of sample means around the true population mean.
To compute the standard deviation of the sampling distribution of the means, one typically divides the population standard deviation by the square root of the sample size.
Therefore, the standard deviation of the sampling distribution of the means is 29/√36 = 29/6 = 4.83 pounds.
So, the sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.
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A company's profit (in millions of dollars) can be represented by y=x^2 -16x +67 where x is the number of years since the company started. When did the company have a profit of 7 million dollars?
For given quadratic equation, the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.
What exactly are quadratic equations?
A quadratic equation is a second-degree polynomial equation of the form:
ax²+ bx + c = 0
where x is the variable and a, b, and c are constants, with a ≠ 0. The term "quadratic" comes from the Latin word "quadratus", which means "square". In other words, a quadratic equation is an equation that involves the square of the variable x.
Now,
We are given that the profit of the company (in millions of dollars) can be represented by the equation y = x² - 16x + 67, where x is the number of years since the company started.
We want to find when the company had a profit of 7 million dollars.
So, we can set y = 7 in the equation:
7 = x² - 16x + 67
Rearranging and simplifying:
x² - 16x + 60 = 0
Now, we can solve for x using the quadratic formula:
x = (-(-16) ± √((-16)^2 - 4(1)(60))) / 2(1)
x = (16 ± √(16)) / 2
x = 8 ± 2
Therefore, the solutions are x = 10 or x = 6.
This means that the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.
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Identify which functions have complex roots by selecting the function names on the provided coordinate plane.
From the graphs in the given coordinate plane, the functions that have complex roots are function b, function d and function f.
Determining the functions that have complex rootsFrom the question, we are to determine the functions that have complex roots in the given coordinate plane.
In a quadratic graph, if the vertex of the quadratic function lies above the x-axis, and the parabola opens upward, there will be NO x-intercepts. The graph will have complex roots.
Also, if the vertex of the quadratic function lies below the x-axis, and the parabola opens downward , there will be NO x-intercepts.
The graph will have complex roots.
In the given coordinate plane, the functions that have complex roots are function b, function d and function f.
Hence, the functions b, d, and f have complex roots.
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Determine the value of x
Answer:
12 × 3 = 36
the top of the diagram will also equal 36
138-72=66
66 ÷2= 33
33÷3 =11
therefore x=11
Answer:
perimeter = 138
p=2(138+12)
p=2×150
p=300
x=300
Karen has two dogs. The larger dog weighs 1. 4 pounds more than the smaller dog. The combined weight of the two dogs is 12. 6 pounds
The weight of the smaller dog is 5.6 pounds.
Let the weight of the smaller dog be x, then,
The weight of the larger dog = 1.4 pounds.
The combined weight of the dogs = 12.6 pounds.
Therefore,
The sum of the weight of the larger dog and smaller dog = the combined weight of the dogs.
That is,
1.4 + x + x = 12.6
1.4 + 2x = 12.6
2x = 12.6 - 1.4
2x = 11.2
x = 11.2 ÷ 2
x = 5.6.
Hence, the weight of the smaller dog is 5.6 pounds.
?
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Your question is incomplete, and the complete question would be:
Karen has two dogs. the larger dog weighs 1.4 pounds more than the smaller dog. the combined weight of the two dogs is 12.6 pounds. what is the weight of the smaller dog?
The table contains the number of M&M’s of each color that were found in a case.
M&M Distribution
Blue Brown Green Orange Red Yellow Total
399 538 364 393 507 351 2552
Round answers to four decimal places, if necessary.
Find the probability of choosing a green or red M&M.
P(green or red) =
Find the probability of choosing a blue, red, or yellow M&M.
P(blue, red, or yellow) =
Find the probability of not choosing a brown M&M.
P(not brown) =
Find the probability of not choosing a green M&M.
P(not green) =
(a) P(green or red) = 0.3946
(b) P(blue, red, or yellow) = 0.7606
(c) P(not brown) = 0.7807
(d) P(not green) = 0.6559
What is probability?
Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.
The total number of M&M's is 2552.
(a) P(green or red) = P(green) + P(red)
= 364/2552 + 507/2552
= 0.2692
(b) P(blue, red, or yellow) = P(blue) + P(red) + P(yellow)
= 399/2552 + 507/2552 + 351/2552
= 0.4917
(c) P(not brown) = 1 - P(brown)
= 1 - 538/2552
= 0.7891
(d) P(not green) = 1 - P(green)
= 1 - 364/2552
= 0.8575
Hence,
(a) P(green or red) = 0.3946
(b) P(blue, red, or yellow) = 0.7606
(c) P(not brown) = 0.7807
(d) P(not green) = 0.6559
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HELPPPPPPPPPPPPpppppppppppppppppppppppp
Answer:C
Step-by-step explanation:
[tex](x-3)^2=5\\we \ should \ find \ square \ root \ of \ each \ side,\\\sqrt{(x-3)^2}=\sqrt{5}\\1)x-3=\sqrt{5}x=\sqrt{5}+3\\2)3-x=\sqrt{5}\\x=3-\sqrt{5}\\\\so,x=3\± \sqrt{5}[/tex]
the daily high temperature for chattanooga is normally distributed with mean 79 and standard deviation 4. find the probability that a randomly chosen temperature is between 70 and 75.
The probability of randomly selecting a temperature between 70 and 75 is approximately 0.8291.
To find the probability that a randomly chosen temperature is between 70 and 75, we need to use the z-score formula as shown below:
z = (x - μ) / σ
Where:x = 70 and 75μ = 79σ = 4z1 = (70 - 79) / 4 = -2.25z2 = (75 - 79) / 4 = -1P(70 < x < 75) = P(-2.25 < z < -1)
To find the probability for the above inequality, we need to use a calculator. We know that the probability of the standard normal distribution is equal to 1.
Hence, P(-2.25 < z < -1) = Φ(-1) - Φ(-2.25) = 0.8413 - 0.0122 ≈ 0.8291. Therefore, the probability is about 0.8291.
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Please I really need help the blank boxes are from 0-9.
For no solution 7x+10
For one solution8x+0
For infinite solution 7x+5
Define infinite solutionAn infinite solution is a solution to a system of equations that has an infinite number of possible solutions. In other words, any value for the variables in the system will satisfy all the equations.
2x+5+2x+3x
On adding the values with variables, x=7
On adding constant values=5
2x+5+2x+3x=7x+5
For no solution
7x+5=7x+10
For one solution
7x+5=8x
x=5
For infinite solution
7x+5=7x+5
Hence, For no solution 7x+10
For one solution 8x+0
For infinite solution 7x+5.
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URGENTTTTT!!!!!!!!!! please complete the chart with the correct angle measures
(numbers 6-9 please!)
Answer:
9 hope u get it right budddyyyy
Leeanne plans to sell her car and places an x-line ad. The newspaper charges p dollars for the
first k lines and e dollars per extra line, to run the ad for a week.
When x > k, write an algebraic expression for the cost of running the ad for a week.
a.
b. When x
Answer:
a. When x > k, the cost of running the ad for a week can be expressed as:
C = p + e(x - k)
where C is the cost in dollars, p is the cost per k lines, e is the cost per extra line, and (x - k) is the number of extra lines over k.
b. When x ≤ k, the cost of running the ad for a week can be expressed as:
C = p
where C is the cost in dollars and p is the cost per k lines. Since the number of lines x is less than or equal to k, there are no extra lines and the cost is simply the base cost of p dollars for k lines.
Hope this helped! I'm sorry if it's wrong. If you need more help, ask me! :]
find the values of a, b, and c in the equation 5x^2-2=2x^2+10x+6
The value οf a = 3, b=-10, c-8
What is quadratic equatiοn?it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm. A nοn-zerο term (a 0) fοr the cοefficient οf x² is a prerequisite fοr an equatiοn tο be a quadratic equatiοn.
The x² term is written first, then the x term, and finally the cοnstant term is written when cοnstructing a quadratic equatiοn in standard fοrm. In mοst cases, the numerical values οf letters a, b, and c are expressed as integral values rather than fractiοns οr decimals.
The equatiοn given 5x²-2=2x²+10x+6
3x²-10x-8=0
values οf a = 3, b=-10, c-8
Hence the value οf a = 3, b=-10, c=8
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Baxter’s Hardware has some followers on their social media account on Friday. On Saturday, the account gains 18 new followers. On Sunday, 20 people stop following the Baxter’s Hardware account. Baxter’s Hardware has 25 followers on Monday morning. The equation f + 18 - 20 = 25 represents the situation. Solve the equation. Be sure to show your work.
Please answer quick!!!
According to given equation Baxter’s Hardware had 27 followers on Sunday morning.
What is equation?
Equations can take many forms, including linear, quadratic, polynomial, trigonometric, and exponential, and can be used to model and solve a wide range of real-world problems.
The given equation is:
f + 18 - 20 = 25
Adding the numbers on the left side, we get:
f - 2 = 25
Adding 2 to both sides, we get:
f - 2 + 2 = 25 + 2
Simplifying, we get:
f = 27
Therefore, Baxter’s Hardware had 27 followers on Sunday morning.
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PLEASE HELP I OS EASY\
Find the surface area of the rectangular prism.
A storage container is in the shape of a rectangular prism. The container has a length of 5 feet, and a width of 9 feet, and a height of 8 feet. What is the surface area of the container?
360 ft2
314 ft2
157 ft2
22 ft2
ANswer __________________
The surface area οf the cοntainer is 314 ft².
What is rectangle?A rectangle is a geοmetric shape that has fοur sides and fοur right angles (90 degrees) with οppοsite sides being parallel and equal in length. It is a type οf quadrilateral, a pοlygοn with fοur sides.
Tο find the surface area οf a rectangular prism, we need tο add the areas οf all six faces. The fοrmula fοr the surface area οf a rectangular prism is:
Surface area = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height οf the rectangular prism.
Substituting the given values, we get:
Surface area = 2(5)(9) + 2(5)(8) + 2(9)(8)
Surface area = 90 + 80 + 144
Surface area = 314 square feet
Therefοre, the surface area οf the cοntainer is 314 ft².
Answer: 314 ft².
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I dont know what 28x76 is
Answer:
28
x 76
----
168 (units digit of 76 multiplied by 28)
1408 (tens digit of 76 multiplied by 28)
----
2128
Therefore, 28x76 is equal to 2128.
Step-by-step explanation:
The pH of a solution is given by the formula pH=−logH+, where H+ is the concentration of hydrogen ions in moles per liter in the solution. Lye has a pH of 12.13. Use this formula to find the hydrogen ion concentration, [H+]. Round to one decimal place if necessary.
Given data:
pH of lye = 12.13
Using the formula pH = -log[H+], we have to find the hydrogen ion concentration, [H+].
Now, putting the given values in the formula, we get:
pH = -log[H+]
12.13 = -log[H+]
log[H+] = -12.13
[H+] = 10^-12.13 = 5.01187 x 10^-13
So, the hydrogen ion concentration, [H+] is 5.01187 x 10^-13 moles/liter. Therefore, the answer is 5.01187 x 10^-13.
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Given: S is on the segment RT. RS = x + 2, ST = 3x + 1, and RT = 15.
On solving the question we have that We can see that RS + ST = RT, equation confirming that S is on segment RT: RT = RS + ST = 5 + 10 = 15
What is equation?A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.
Because S is on the section RT, we know that RS + ST = RT. As a result, we may construct the following equation:
RS + ST = 3x + 1 + (x + 2) = 15
To simplify this equation, we can combine similar terms:
4x + 3 = 15
Subtraction of 3 from both sides yields:
4x = 12
When we divide both sides by 4, we get:
x = 3
RS = x + 2 = 5 and ST = 3x + 1 = 10 as a result.
We can see that RS + ST = RT, confirming that S is on segment RT:
RT = RS + ST = 5 + 10 = 15
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Harrison has a rectangular plank of wood that is 29 inches long. He creates a ramp by resting the plank against a wall with a height of 14 inches, as shown. Using Pythagoras' theorem, work out the horizontal distance between the wallI and the bottom of the ramp. Give your answer in inches to 1 d.p.
Answer:
Horizontal distance between the wall and the bottom of ramp = 25.4 inches.
Step-by-step explanation:
Pythagorean theorem:
AB -> wall ; AB = 14 inches
AC -> Wooden plank ; AC = 29 inches
BC -> horizontal distance between the wall and the bottom of ramp(pank).
Pythagorean theorem,
[tex]\boxed{\bf base^2 + altitude^2 = hypotenuse^2}[/tex]
BC² + AB² = AC²
BC² + 14² = 29²
BC² + 196 = 841
BC² = 841 - 196
= 645
BC = √645
BC = 25.4 inches
Horizontal distance between the wall and the bottom of ramp = 25.4 inches.
Given,
Length = 29 inches
Height = 14inches
Here,
Pythagorean theorem:
AB -> wall ; AB = 14 inches
AC -> Wooden plank ; AC = 29 inches
BC -> horizontal distance between the wall and the bottom of ramp (plank).
Pythagorean theorem,
Base² + Perpendicular² = Hypotenuse²
BC² + AB² = AC²
BC² + 14² = 29²
BC² + 196 = 841
BC² = 841 - 196
= 645
BC = √645
BC = 25.4 inches
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Using Unit Rates to compare Ratios continued
5 Branden and Pete each play running back. Branden carries the ball 75 times for
550 yards, and Pete has 42 carries for 380 yards. Who runs farther per carry?
Pete did more his outcome was 9. 0 which was bigger the branden do
380 divided by 42 for your answer
Pete runs farther per carry, with a unit rate of 9.05 yards per carry compared to Branden's unit rate of 7.33 yards per carry.
A unit rate is a rate that has a denominator of 1. It is a ratio that compares a quantity to its unit of measurement.
To determine who runs farther per carry, we can use unit rates to compare the distance each player runs per carry.
For Branden:
Distance per carry is
= 550 yards ÷ 75 carries
Divide the numbers
= 7.33 yards per carry
For Pete:
Distance per carry is
= 380 yards ÷ 42 carries
Divide the numbers
= 9.05 yards per carry
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help me find the missing sides to solve this equation
For the equilateral triangles we have:
1) x = 5, y = √50
2) a = 2, b = √8
3)y = 8, x = √128
4) a = b = 7/√2
How to find the missing sides?We can see some triangles, remember that for a right triangle whose angles are 45°, we have an equilateral triangle.
So the two legs have the same measure.
1) Here we can see that x = 5, and the hypotenuse is given by:
y^2 = 5^2 + 5^2
y^2 = 50
y = √50
2) Here we have a = 2, then the hypotenuse is:
b^2 = 2^2 + 2^2
b^2 = 8
b = √8
3) Here we have y = 8, then the hypotenuse is:
x^2 = 8^2 + 8^2
x^2 = 128
x = √128
On the last triangle we can see that the hypotenuse is 7, and we know that a = b
then:
7^2 = a^2 + b^2
7^2 = a^2 + a^2
49 = 2*a^2
(49/2) = a^2
√(49/2) = a
7/√2 = a = b
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Divya is cooking dinner. she goes to the market to buy ingredients. the price per pound of different ingredients is shown in the table below. Diyva recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2 pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus How much will diyva pay for all the ingredients in the recipe?
Step-by-step explanation:
Divya is cooking dinner. she goes to the market to buy ingredients. the price per pound of different ingredients is shown in the table below. Diyva recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2 pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus How much will diyva pay for all the ingredients in the recipe?
the basis for using a normal probability distribution to approximate the sampling distribution of the sample means and population mean is . a. the empirical rule b. chebyshev's theorem c. bayes' theorem d. the central limit theorem
The cοrrect answer tο the given questiοn is d. the central limit theοrem.
What is frequency distributiοn?The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.
The basis fοr using a nοrmal prοbability distributiοn tο apprοximate the sampling distributiοn οf the sample means and pοpulatiοn mean is the central limit theοrem.
The central limit theοrem states that fοr a sufficiently large sample size, the sampling distributiοn οf the sample means will be apprοximately nοrmal, regardless οf the shape οf the pοpulatiοn distributiοn. This theοrem allοws us tο make statistical inferences abοut the pοpulatiοn mean based οn the sample mean using the prοperties οf the nοrmal distributiοn, such as the mean and standard deviatiοn.
Therefοre, the cοrrect answer tο the given questiοn is d. the central limit theοrem.
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How many terms are in the expression: 12p + 8m + 2
Answer: I THINK 4.
Step-by-step explanation:
Sorry if it is wrong!! :'D
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
The answer is B
Step-by-step explanation:
I choose 10 consecutive numbers. if I exclude one of the numbers the remaining 9 sum to 2023 which number did I exclude?
Answer:
the number 228
Step-by-step explanation:
Let's call the smallest number in the consecutive sequence "x". Then, the 10 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, and x+9.
If we exclude one of these numbers, then the sum of the remaining 9 numbers would be:
(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) or 9x + 36.
We know that the sum of the remaining 9 numbers is 2023, so we can set up the equation:
9x + 36 = 2023
Solving for x, we get:
9x = 1987
x = 221
Therefore, the smallest number in the consecutive sequence is 221, and the 10 numbers are 221, 222, 223, 224, 225, 226, 227, 228, 229, and 230.
If we exclude the number 228, then the sum of the remaining 9 numbers is 2023.
Let X be a normally distributed random variable. Given that the
mean is 2 and P(X < 2.24) = 0.7257, what is the variance?
a. 0.5266
b. None of the suggested answers are correct
c. 0.6
d. 0.4
e. 0.1
e [0.1}
We know that P(X < 2.24) = 0.7257. Also, the mean is 2.Let us calculate the variance of the given normal distribution random variable. Given that P(X < 2.24) = 0.7257, we have to find variance. Let us solve this question as follows:We know that mean of normally distributed random variable is μ and standard deviation is σ. As the mean is 2, μ = 2.We have the z-score: z = (2.24 - 2) / σFrom the normal distribution table, we can find out that P(Z < 0.80) = 0.7881Now, we have the following equation:0.7881 = (2.24 - 2) / σσ = 0.3158Finally, we can find the variance (σ^2) = 0.3158^2 = 0.0995 ≈ 0.1Therefore, the correct answer is option e. 0.1.
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