Answer:
(a) 0.0668
(b) $638.74
Step-by-step explanation:
Let X denote the tips earned by a waiter.
It is provided that X follows a left-skewed distribution with mean, μ = $10.60 and standard deviation, σ = $6.60.
It is also provided that, the waiter usually waits on about n = 50 parties over a weekend of work.
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,
[tex]\mu_{S}=n\mu\\[/tex]
And the standard deviation of the distribution of the sum of values of X is given by,
[tex]\sigma_{S}=\sqrt{n}\sigma[/tex]
As the sample size is large, i.e. n = 50 > 30, the Central Limit Theorem can be used to approximate the sampling distribution of total tips by the normal distribution.
The mean and standard deviation are:
[tex]\mu_{S}=50\times 10.60=530\\\\\sigma_{S}=\sqrt{50}\times 6.60=46.67[/tex]
(a)
Compute the probability that he will earn at least $600 as follows:
[tex]P(S\geq 600)=P(\frac{S-\mu_{S}}{\sigma_{S}}\geq \frac{600-530}{46.67})\\\\=P(Z>1.50)\\\\=1-P(Z<1.50)\\\\=1-0.93319\\\\=0.06681\\\\\approx 0.0668[/tex]
Thus, the probability that he will earn at least $600 is 0.0668.
(b)
Let x represents his earnings on the best 1% of such weekends.
That is, P (X < x) = 0.99.
⇒ P (Z < z) = 0.99
The corresponding z-score is, 2.33.
Compute the value of x as follows:
[tex]z=\frac{S-\mu_{S}}{\sigma_{S}}\\\\2.33=\frac{x-530}{46.67}\\\\x=530+(2.33\times 46.67)\\\\x=638.7411\\\\x\approx 638.74[/tex]
Thus, on the best 1% of such weekends the waiter earned $638.74.
The sales tax for an item was $18.60 and it cost $ 310 before tax. Find the sales tax rate. Write your answer as a percentage.
You are trying to determine if you should accept a shipment of eggs for a local grocery store. About 4% of all cartons which are shipped have had an egg crack while traveling. You are instructed to accept the shipment if no more than 10 cartons out of the 300 you inspect have cracked eggs. What is the probability that you accept the shipment? (In other words, what is the probability that, at the most, you had 16 cartons with cracked eggs?)
a. 1012.
b. 3669.
c. 5319.
d. 4681.
e. 5832.
f. 6331.
Answer:
0.8809
Step-by-step explanation:
Given that:
The population proportion p = 4% = 4/100 = 0.04
Sample mean x = 16
The sample size n = 300
The sample proportion [tex]\hat p =\dfrac{x}{n}[/tex]
= 16/300
= 0.0533
∴
[tex]P(\hat p \leq 0.0533) = P\bigg ( \dfrac{\hat p - p}{\sqrt{\dfrac{P(1-P)}{n}}}\leq\dfrac{0.0533 - 0.04}{\sqrt{\dfrac{0.04(1-0.04)}{300}}}\bigg )[/tex]
[tex]P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{\sqrt{\dfrac{0.04(0.96)}{300}}}\bigg )[/tex]
[tex]P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{\sqrt{\dfrac{0.0384}{300}}}\bigg )[/tex]
[tex]P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{\sqrt{1.28 \times 10^{-4}}}\bigg )[/tex]
[tex]P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{0.0113}}\bigg )[/tex]
[tex]P(\hat p \leq 0.0533) = P\bigg ( Z\leq1.18}\bigg )[/tex]
From the z tables;
= 0.8809
OR
Let X be the random variation that follows a normal distribution;
Then;
population mean [tex]\mu[/tex] = n × p
population mean [tex]\mu[/tex] = 300 × 0.04
population mean [tex]\mu[/tex] = 12
The standard deviation [tex]\sigma = \sqrt{np(1-p)}[/tex]
The standard deviation [tex]\sigma = \sqrt{300 \times 0.04(1-0.04)}[/tex]
The standard deviation [tex]\sigma = \sqrt{11.52}[/tex]
The standard deviation [tex]\sigma = 3.39[/tex]
The z -score can be computed as:
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]
[tex]z = \dfrac{16 -12}{3.39}[/tex]
[tex]z = \dfrac{4}{3.39}[/tex]
z = 1.18
The required probability is:
P(X ≤ 10) = Pr (z ≤ 1.18)
= 0.8809
The diameter of a circle is 44 what’s the radius
Answer:
22
Step-by-step explanation:
Look at image which graph shows T (ABC)?
Answer:
A.
Step-by-step explanation:
That is a translation of 3 units left and 6 units down.
write a linear equation in slope intercept form for a line that passes through the point 6,-2 and has a slope of -2/3
y=0.625x+1.75 is the equation for your problem.
HELP ME OUT REALL FAST PLEASEE
Answer:
The answer is C because you have to multiply them both:)
Answer:
The answer is C
Step-by-step explanation:
What I'm about to write is overkill for this question, but it works for any common denominator. Factor the denominators.
10: 2 * 5
5 : 1 * 5
You need 1 five and 1 two. The answer is 10
The correct way to go about doing the question is to multiply the 5 by 2 and the 2 on top by 2
2*2/5*2 = 4/10
1/10 1 / 10
4/10 + 1/10
Amaia purchased two blouses and a skirt for a total of $32. The sales tax rate is 8%. How much total sales tax will Amaia pay on these items?
Answer:
2.56
Step-by-step explanation:
8% of 32 is 2.56
Tom is the custodian at the local highschool. He has a circular key ring with 9 keys on it. How many different arrangements of those keys can Tom make on his key ring?
tom will have his key 10
Answer:
40,320.. took the test on USA test prep
Step-by-step explanation:
Help plsssssssssssssssssssssss
Please give me the correct answer.
Answer:
33
Step-by-step explanation:
If an initial amount A0 of money is invested at an interest rate i compounded times a year, the value of the investment after t years is If we let n = 8, that is referred to as the continuous compounding of interest. Use L' Hospital's Rule to show that if interest is compounded continuously, then the amount after years is A=A0eit
Answer:
Following are the solution to the given point:
Step-by-step explanation:
Please find the comp[lete question in the attached file.
Given:
[tex]\bold{ \lim_{n \to \ \infty} (1+ \frac{r}{n})^{nt} =e^{rt}}[/tex]
In point 1:
[tex]\to y = (1+ \frac{r}{n})^{nt}[/tex]
In point 2:
[tex]\to \ln (y)= nt \ln(1+ \frac{r}{n})[/tex]
In point 3:
Its key thing to understand, which would be that you consider the limit n to[tex]\infty[/tex], in which r and t were constants!
[tex]=lim_{n \to \ \infty} \ln (y) = lim_{n \to \ \infty} nt \ln(1+\frac{r}{n})\\\\= lim_{n \to \ \infty} \frac{\ln(1+\frac{r}{n})}{\frac{1}{nt}}\\\\= lim_{n \to \ \infty} \frac{\frac{-r}{\frac{n^2}{(1+\frac{r}{n})}}}{- \frac{1}{n^2t}}\\\\= lim_{n \to \ \infty} \frac{\frac{rn^2t}{n^2}}{(1+\frac{r}{n})}\\\\= lim_{n \to \ \infty} \frac{rt}{(1+\frac{r}{n})}\\\\= \frac{rt}{(1+\frac{r}{0})}\\\\=rt[/tex]
In point 4:
[tex]\to \lim_{n \to \ \infty} = (1+\frac{r}{n})^{nt}[/tex] and
[tex]\to \lim_{n \to \ \infty} = A_0e^{rt}[/tex]
Point B (-5,5) is
reflected over the
x-axis. Where is
B'?
Answer:
(-5,-5)
Step-by-step explanation:
The table below represents equivalent ratios.
X y
6= 10
12 = 20
??= 45
Answer:
27
Step-by-step explanation:
6/10=12/20 because when you cross multiply, 120=120, so then you can do wither 6/10=x/45 and when you cross multiply you get 270=10x and 270/10=27.
The Buffalo Bills football team wanted to buy new footballs. what did the team have to pay per football? Be sure to explain all of your work.
Answer: I don't see the amount per football
Step-by-step explanation:
here is a list of number 51 38 48 36 39 40 39 47
WHAT is the median
Answer:
36
Step-by-step explanation:
Median is the Middle number in the sequence.
Hope this Helps!!
:D
A snowboard shop charges $10, plus an additional #3 per hour to rent a snowboard. Write the equation for the line in slope-intercept form.
HURRY HELP PLS!!
Answer:
y = 3x + 10
Step-by-step explanation:
Answer:
im pretty sure it is (0,5) or (10,0)
Step-by-step explanation:
A triangle has angles that measure 54.6° and 17.8°. Which equation can be used to find the value of x, the measure of the third angle in the triangle?
Answer:
58.6 + 17.8 + x = 180
Step-by-step explanation:
hope this helps
Solve the following equations for x.
kx - b=3d + 7b
Answer:
x= 3d/k +8b/k i think
Step-by-step explanation:
2. Which of the following gives a valid reason for using the given
solution method to solve the system of equations shown?
Equation 1: 4x - 5y = 4
Equation li: 2x + 3y = 2
a Elimination; a coefficient in Equation is an integer multiple of a coefficient
in Equation II.
b Elimination; a coefficient in Equation II is an integer multiple of
a coefficient in Equation 1
c Substitution; equation I can be solved for x in one step by dividing both
sides by 4
d Substitution; equation can be solved for x in one step by subtracting 3y
from both sides.
Answer:
A. Elimination; a coefficient in Equation I is an integer multiple of a coefficient
in Equation II.
Step-by-step explanation:
4 is a multiple of 2. Therefore, the answer would be A.
A genetic experiment with peas resulted in one sample of offspring that consisted of 438 green peas and 173 yellow peas.
Required:
a. Construct a 95â% confidence interval to estimate of the percentage of yellow peas.
b. It was expected thatâ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is notâ 25%, do the results contradictâ expectations?
Answer:
a
The 95% confidence interval is [tex] 0.2474 < p < 0.3188 [/tex]
b
The result obtained does not contradict expectation
Step-by-step explanation:
From the question we are told that
The number of green peas is k = 438
The number of yellow peas is u = 173
Generally the sample size is mathematically represented as
[tex]n = k + u[/tex]
=> [tex]n = 438 + 173[/tex]
=> [tex]n = 611[/tex]
Generally the sample proportion for yellow peas is
[tex]\^ p = \frac{u}{n}[/tex]
=> [tex]\^ p = \frac{173}{611 }[/tex]
=> [tex]\^ p = 0.2831[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 1.96 * \sqrt{\frac{ 0.2831 (1- 0.2831)}{611} } [/tex]
=> [tex]E = 0.0357 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex] 0.2831 -0.0357 <p< 0.2831 + 0.0357[/tex]
=> [tex] 0.2474 < p < 0.3188 [/tex]
From the question we are told that it was expected that 25% of the offspring peas will be yellow
Now from the 95% confidence interval obtained we see that the expected sample proportion(25% ) falls within it so it means that the result obtained does not contradict expectation
8. Kim has a fever. Her temperature is 100.5 degrees Fahrenheit. Norr
temperature is 98.6 degrees Fahrenheit, How much above normal
temperature is Kim's fever?
Answer:
1.9 degrees above the normal temperture
Step-by-step explanation:
Normal temperture: 98.6 degrees Fahrenheit
100.5 - 98.6 = 1.9
20POINTS WILL MARK BRANLIEST PLSS
The layout of a city park is pictured in the figure above. Park managers would like to find the distance of segment DE, in order to build a walkway across the middle of the park. The park managers look up the distance of segments BC and AB in the city records. If the length of segment AB is determined to be 562 feet, what is the distance of mid-segment DE in feet?
Select one:
A. 220
B. 244
C. 276
D. 281
Does f(x)=|x|+5 go up or down
Answer:
up
Step-by-step explanation:
postive, up!
Answer:
..........UP..........
What is the multiplicative inverse of 1 2/3
Answer:
sorry if im wrong but im pretty sure -5/3
Step-by-step explanation:
Answer:
2/1
Step-by-step explanation:
A calculator showed me that this was the answer. I would give you the link but I would probably get deleted. I already got warned so yeah.
Hope this helps!
What is the polynomial of least degree with the given zeroes -2 and 4?
Answer:
-2
Step-by-step explanation:
base on my stuck knowledge
Jason used a graphing tool to find the equation of the line of best fit in this scatter plot. After reading the equation of the line from the graphing tool, Jason wrote in his notebook that the line of best fit is represented by the equation y = 0.316x + 9.105. Jason likely an error when writing the equation in his notebook because the slope and the y-intercept of the equation he wrote.
Answer: Jason likely MADE an error when working the equation in his notebook because ONLY THE Y-INTERCEPT MATCHES the slope and the y-intercept of the equation he wrote.
Step-by-step explanation:
-2(b+5)= -6
What is b?
Answer:
-2
Step-by-step explanation:
It would be =
-2(-2 + 5) = -6
4 - 10 = -6
-10 and a positive four is a -6
PLEASE HELP ASAP
Given the information in the diagram below, find the measure of angle N. Use complete sentences to show how you found this answer. In your written response, include key vocabulary terms.
Answer:
76
Step-by-step explanation:
j and k are the same size and every triangle equals 180
64+64=128
180-128=52
L=52
l and m are the same
52+52=104
180-104= 76
n=76
It takes 1 minute for a high speed train to travel 2 miles. How many miles can it travel in 1 hour?
150 adults complete a survey 80
are women
Answer:
70 men
Step-by-step explanation:
We can subtract to find the amount of men who took the survey.
150 - 80 = 70
Best of Luck!