A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 3 inches. A random sample of 41 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)

Answers

Answer 1

Answer:

0.5160

Step-by-step explanation:

Let us assume that the length of fishes in the tank is normally distributed. Thus, x is the random variable representing the length of fishes in the tank. Since the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = standard deviation

number of samples

From the information given,

µ = 15

σ = 4

n = 31

We want to find the probability that x is between (15 - 0.5) inches and (15 + 0.5) inches. The probability is expressed as

P(14.5 ≤ x ≤ 15.5)

For x = 14.5

z = (14.5 - 15)/(4/√31) = - 0.7

Looking at the normal distribution table, the probability corresponding to the z score is 0.2420

For x = 15.5

z = (15.5 - 15)/(4/√31) = 0.7

Looking at the normal distribution table, the probability corresponding to the z score is 0.7580

Therefore,

P(14.5 ≤ x ≤ 15.5) = 0.7580 - 0.2420 = 0.5160


Related Questions

I would appreciate it if you can help me with this.

Answers

Answer:

[tex]450000 \leqslant 15000 + 4t[/tex]

The product two consecutive odd numbers is 63find the number

Answers

Answer:

These results, 7 and 9, have a product of 63, as stated.

Step-by-step explanation:

Represent the first odd number by x and the first consecutive odd number by x + 2.  Then the product of these two numbers is x(x + 2) and it equals 63.

Solve for x.  Perform the indicated multiplication, obtaining

x^2 + 2x - 63 = 0

Solve this by factoring:  (x + 9)(x - 7) = 0

Then x could be either -9 or +7.  If we let x = 7 then the first consecutive odd number is 7 + 2, or 9.  These results, 7 and 9, have a product of 63, as stated.

A can contains 48 cups of fruit juice. How many gallons of fruit juice does the can contain?

Answers

Answer:

3

Step-by-step explanation:

How do you know 72/80 is greater than 7/8? Explain

Answers

Answer:

Step-by-step explanation: I know that 72/80 is greater than 7/8 because when we make 7/8 as the same denominator as of 72/80 it is only 70/80 which is smaller than 72/80.

x/5 - 74 = 26

what is x​

Answers

Step-by-step explanation:

x/5 - 74 = 26

x/5 = 26 + 74

x/5 = 100

x = 100 x 5

x = 500

Is 1 1/30 more or less then 1 1/2 gallons

Answers

Answer:

less

Step-by-step explanation:

1/30 is less than 1 1/2 gallons

What is the answer to: 1a to the power of 349 b to the power of 28 c to the power of 2 d to the power of 82 e to the power of 48 f to the power of 920 g to the power of 40 h to the power of 38 i to the power of 492 j to the power of 23 k to the power of 43 l to the power of 982 m to the power of 48 n to the power of 62=(4/2 x 10 x(the square root of 100)

Answers

Answer:

Its 7.908764333

Step-by-step explanation:

Trust me :)

What is greater 7 or -7

Answers

7 is greater because it’s a positive and above 0, -7 is under 0 which is considered a negative

Hello there!

7 is greater than -7, because positive numbers are always greater than negative ones.

a>-a

The > sign means "greater than"

Hope it helps.

~A lonely teen who helps others with a smile

-Grace :-)

Good luck.

is the equation in the picture true or false?

Answers

Answer:

false

Step-by-step explanation:

I hope this helps!!

What should the IUPAC name for a binary covalent compound lack? prefixes Roman numerals an -ide ending the name of a nonmetal.​

Answers

The  IUPAC name for a binary covalent compound lack prefixes such as mono, di, tri tetra etc.

A binary compound is a compound that is composed of only two elements. Many binary compounds could be made up of a metal and a nonmetal or even two nonmetals as the case may be. Examples of binary compounds include; SO2, NaH, K2S etc.

We must note that a binary covalent compound uses Roman numerals to indicate the oxidation state of the central atom in the compound. For instance, SO2 is called Sulfur IV oxide.

Hence, the  IUPAC name for a binary covalent compound lack prefixes such as mono, di, tri tetra etc.

Lear more about IUPAC: https://brainly.com/question/11587934

Someone please help this is soooooo hard

Answers

Step-by-step explanation:

1. 10x-7=5x+3; ⇒ 5x=10; ⇒ x=2. If x=2, then

2. QS=10*2-7=14;

3. SR=5*2+3=13;

4. m(∠PSR)=15*2+42=72°;

5. m(∠PSQ)=180-m∠(PSR)=180-72=108°.

What happens to the value of the expression 20 + a, a as a increases?

Answers

Answer:

With the increase of the value of a ,the value of the expression 20+a will also increase.

Step-by-step explanation:

helpp :(
Habib rides his bike to school. This describes his trip:

A. Rides toward school
B. Stops to wait for a friend
C. Rides the rest of the way to school

Drag one segment to each box to show the shape of the graph of Habib's distance from home for each interval of time.

Answers

The only pattern that would make sense is A- option 3 (/), B- option 1 (-), C- option 3 again (/). Hope this helps!

Answer:

see

Step-by-step explanation:

Ben worked 5 hours at x dollars per hour. Julie worked 8 hours
and earned twice as much as Ben per hour. Phil worked 10
hours and earned 4 dollars an hour less than Julie. Choose the
expression that is correctly simplified and best represents
their total wages.
A. 31x - 4
B. 31x – 40
C. 41x - 10
D. 41x -40

Answers

Answer: D

Explanation:

Ben : 5 • x = 5x
Julie: 8 • 2x = 16x
Phil: 10 • (2x - 4) = 20x - 40

Add them all together:

5x + 16x + 20x - 40
= 41x - 40

. A circulating pump consumes 450 W for 24 hr a day. a. Determine the energy consumed for a one-year period. b. Calculate the utility energy charges for this period at a rate of $0.12/kWh. c. Determine the energy saved for a one-year period, if the pump is switched off 8 hr a day. d. Calculate the energy cost savings for this period at a rate of $0.12/kWh, if the pump is switched off 8 hr a day.

Answers

Answer:

  a. 3942 kWh

  b. $473.04

  c. 1314 kWh

  d. $157.68

Step-by-step explanation:

a.

There are 1000 W in 1 kW, so 450 W = 0.450 kW. The energy used per day is ...

  (0.45 kW)(24 h) = 10.8 kWh . . . . energy per day

Then in a 365-day year, the energy used is

  (365 da/yr)(10.8 kWh/da) = 3942 kWh/yr

__

b.

At the rate of $0.12/kWh, the cost of running the pump is ...

  ($0.12/kWh)(3942 kWh/yr) = $473.04/yr

__

c.

Switching the pump off for 1/3 of the time will save 1/3 of the energy found in part (a):

  1/3(3942 kWh) = 1314 kWh . . . . energy saved by switching off the pump

__

d.

The savings will be 1/3 of the cost of running the pump full time:

  1/3($473.04/yr) = $157.68/yr

i believe X=4, but i could be wrong with the whole thing

Answers

Answer:

A. x = 4

B. RQ = 6

C. 48 square units

Step-by-step explanation:

A. 3x - 2 = 10

3x = 12

x = 12/3

B. a^2 + b^2 = c^2

8^2 + b^2 = 10^2

64 + b^2 = 100

b = sqrt (100 - 64

b = 6

C. Area of a triangle = (b*h)/2

b = (2)(6) = 12

Area = (12 * 8)/2 = 48 square units

please pick the right anwers no bots please

Answers

Answer:

1. 2/3

2. 0

3. 7/2

4. -2

5. -2

6. 1

7. -4/3

8. Undefined

9. 8

10. 9/5

If the sales tax in a town is 5% and Amanda pays $10 in tax on her purchase what was the cost of the item?

Answers

Answer:

$200

Step-by-step explanation:

If the tax is 5%, then she pays $5 for every $100. If she paid $10 in tax, her purchase was $200.

I need help with this math help please!

Answers

Answer: R= 7

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf t = 7}[/tex]

Step-by-step explanation:

-8 (4 - t) = 24

-32 + 8t = 24

Add 32 to both sides

8t = 24 + 32

8t = 56

Divide both sides by 8

t = 7

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

help!! due tommorrow

Answers

Answer:

a and d

Step-by-step explanation:

these simplify to .77 for A and .81 for B

Eugene is purchasing clothing to make different outfits. Each outfit consists of a top, a bottom and a pair of shoes. Eugene found 2 pairs of shoes and 4 bottoms he would like to purchase. What is the minimum number of tops Eugene needs to purchase to make at least 35 different outfits? Express your answer as a whole number.​

Answers

Answer:

70

Step-by-step explanation:

the average score of the five tests was 83. The first 4 scores were 91, 78, 86, 72. What was the score of the 5th test. Thank you so much!

Answers

Answer:

88

Step-by-step explanation:

75% of 32 students are interested in Mathematics. How many are not interested in Mathematics ?

Answers

Answer:

The answer is 8!

Step-by-step explanation:

75% is 3/4 of 100 so you take 32÷4 and get 8, hope this helps:)

75% of 32 students are interested in Mathematics.Therefore, number of students who are interested in Mathematics [tex] = 75\% \: \: of \: \: 32 \\ = \frac{75}{100} \times 32 \\ = \frac{3}{4} \times 32 \\ = 3 \times 8 \\ = 24[/tex]So, number of students interested in Mathematics is 24.Therefore, number of students who are not interested in Mathematics = 32 - 24 = 8So, 8 students are not interested in Mathematics.

Alternative method:

Percentage of students who are interested in Mathematics = 75%Then, percentage of students who are not interested in Mathematics = (100 - 75)% = 25%Therefore, number of students who are not interested in Mathematics [tex] = 25\% \: \: of \: \: 32 \\ = \frac{25}{100} \times 32 \\ = \frac{1}{4} \times 32 \\ = 1 \times 8 \\ = 8[/tex]

Answer:

8

Hope you could get an idea from here.

Doubt clarification - use comment section.

5) If 5 times a number is increased by 4, the result is at least 19. Find the least possible
number that satisfies these conditions.

Answers

Answer:3

Step-by-step explanation:

5x3=15

15+4=19

BRAINLIEST!Blake is the Human Resources manager for a correctional facility. What is one task that Blake might have as part of his job?

A.
confirming appointments for the director of the facility

B.
looking over the costs of new supplies for the facility

C.
mediating a dispute between two employees

D.
organizing the outdoor video surveillance of the facility

Answers

The answer is A confirming appointments for the director of the facility

Answer:

Organising the outdoor video surveillance

Step-by-step explanation:

See he is a manager.

His work is to take care of all resources of companyVideo surveillance must be used for security

PLEAZEEE HELP ME PLS WILL GIVE BRAINLIEST

Answers

Answer:

2q+7r+8

Step-by-step explanation:

(q+3)+(q+2)+(7r+3)

Brainliest is very apprieciated!

find the volume of this prism​

Answers

Answer:

264 cm³

Step-by-step explanation:

Sheri is making 4 pounds of mixed nuts. She will use One-third the amount of macadamia nuts as she does almonds. A graph titled Sheri's Mixed Nut Recipe has pounds of macadamia nuts on the x-axis, and pounds of almonds on the y-axis. 2 lines intersect at (1, 3). How many pounds of each nut will she use? 1 pound of macadamia nuts; 3 pounds of almonds 3 pounds of macadamia nuts; 1 pound of almonds 4 pounds of macadamia nuts; no almonds 4 pounds of almonds; no macadamia nuts.

Answers

1 pound of macadamia nuts; 3 pounds of almonds of each nut will she use.

Given that,

Sheri is making 4 pounds of mixed nuts.

She will use One-third the number of macadamia nuts as she does almonds.

A graph titled Sheri's mixed nut recipe has pounds of macadamia nuts on the x-axis, and pounds of almonds on the y-axis. 2 lines intersect at (1, 3).

We have to find,

How many pounds of each nut will she use?

According to the question,

Total mixed nuts are 4 pounds,

She will use One-third the number of macadamia nuts as she does almonds.

2 lines intersect at (1, 3).

Therefore,

Sheri's mixed nut recipe has pounds of macadamia nuts on the x-axis,

At x-axis, the point 1 lies.

So, macadamia nuts have 1 pound.

And pounds of almonds on the y-axis,

At y-axis, the point 3 lies.

So, almond nuts have 3 pounds.

Hence, 1 pound of macadamia nuts; 3 pounds of almonds of each nut will she use.

For more details about Graphs refer to the link given below.

https://brainly.com/question/9351049

Answer:

A/ the first one

Step-by-step explanation:

Did the edg

help please!!!!! I need it ​

Answers

Answer:

it is 7x-4

Step-by-step explanation:

How do I solve this please look for the x and then the y

Answers

Answer:

x + y = 75

Step-by-step explanation:

2x - 5 and 75 are adjacent angles on a straight line and sum to 180° , that is

2x - 5 + 75 = 180

2x + 70 = 180 ( subtract 70 from both sides )

2x = 110 ( divide both sides by 2 )

x = 55

Then

2x - 5 = 2(55) - 5 = 110 - 5 = 105

2x - 5 and 4y + 25 are vertically opposite angles and are congruent, so

4y + 25 = 105 ( subtract 25 from both sides )

4y = 80 ( divide both sides by 4 )

y = 20

Then x + y = 55 + 20 = 75

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