The average age of all the JSOM students is 24 years with a standard deviation of 9 years. Of 8,000 students, a random sample of 36 students is selected. What is the probability that the sample mean will be between 25.5 and 27 years?

Answer:

The probability that the sample mean will be between 25.5 and 27 years is 0.1359.

Step-by-step explanation:

Let X denote of age of JSOM students.

The information provided is:

[tex]\mu=24\\\sigma=9\\n=36[/tex]

According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu\\[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

As the sample size is large, i.e. n = 36 > 30, the sampling distribution of the average age of all the JSOM students can be approximated by the normal distribution.

Compute the probability that the sample mean will be between 25.5 and 27 years as follows:

[tex]P(25.5<\bar X<27)=P(\frac{25.5-24}{9/\sqrt{36}}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{27-24}{9/\sqrt{36}})\\\\=P(1<Z<2)\\\\=P(Z<2)-P(Z<1)\\\\=0.97725-0.84134\\\\=0.13591\\\\\approx 0.1359[/tex]

Thus, the probability that the sample mean will be between 25.5 and 27 years is 0.1359.

A fencewill go around a circular Garden. The radius of the garden is 29 feet what length of fence is needed

Anybody know how to solve for Y

Anthony has t tickets. Charlie has 2 less than triple the number of tickets that Anthony has. In terms of t, how many tickets does Charlie have?​

A company refinishes wood floors for $1.50 per square foot. Makayla hires the company to refinish 1,000 square feet
in her home. How much does she pay for the refinishing work?
$500
$1,000
$1,500
$5,000

A scientist is examining a multicellular organism that has the ability to move from one location to another and eats food to gain energy for survival. What kingdom would be the best option when classifying this organism?

Opps- THIS IS DUE IN 7 MINS HALPPPPP!!!! I FORGOT TO DO THIS AND NOW I NEED HALPPPP

ps. Giving 30 points if answer is given

Write the standard form of the line that has a slope of −3/4 and y-intercept of −2. Include your work in your final answer.

which one is greater 140% or 0.14

Please help if you can. I will give you a brainliest !!

The square shown has sides of length 6z^7 decimeters. Find it’s area

What is 40/4.



From this_guy

What is the slope and y-intercept of the equation on this graph

You are walking from home to music store. You stop for a rest after 2/3 miles. The music store is actually 3/4 miles from home. How much farther do you have to walk

helppppp please I will give brainliest​

Twelve large bottles of water cost $9. a. How many bottles can you buy for $3?

The table shows the weekly profits of a fruit
vendor. What is the mean profit for these weeks?
Week
1
2
3
4
Profit -$125 -$86
$54
- $35
The mean profit is $

please help and I will mark big brain ​

A landlord owns 3 condominiums, a 1-bedroom condo, a 2-bedroom condo, and a 3-bedroom condo. The total rent she receives is $1240. She needs to make repairs on the condos, and it costs 10% of the 1-bedroom condo’s rent for its repairs, 20% of the 2-bedroom for its repairs, and 30% of the 3-bedroom condo’s rent for its repairs. The total repair bill was $276. The 3-bedroom condo’s rent is twice the 1-bedroom condo’s rent. How much is the rent for all three condos?

What is the slope of line m?

A college student takes the same number of credits each semester. She had 9 credits when she started, and after 6 semesters, she had 117 credits.

BRAINLIEST TO THE CORRECT ANSWER PLEASE HELP ME I BEG U
Chelsea's catering company charges a fixed rate for each hour of an event they work plus a set-up fee. The total cost (C) of the company's last 4 events according to the total hours (h) they worked is found
in the table above.

Which statement is the best representation of the total cost to hire Chelsea's catering company?
A.C= 100* + 25
B. C = 75h + 325
C.C= (100 + 75)"
D. C- 100 + 75h
PLS HELP

please help me :(
Jill, Grace, and Billy shared pennies in the ratio 2 : 4 : 4. They had a total of 120 pennies in all. How many pennies did Jill receive?

2 pennies

24 pennies

48 pennies

60 pennies

May y'all please help me

8


Find the circumference of the circle pictured above.

Round your answer to the nearest tenth

Harry needs 21 square meters of fabric for every 6 wizard cloaks he makes. Complete the table using equivalent ratios. help me pleaseeee

Find the measure of the arc or angle indicated. Assume GE is the diameter of
the circle
O 70°
0 47
O 54
O 60°

A coin is tossed 5 times; find the probability of getting at least 1 tail. Would you consider this event likely to happen?

(08.01)Two lines, A and B, are represented by the following equations:

Line A: 2x + 2y = 8
Line B: x + y = 3

Which statement is true about the solution to the set of equations?

It is (1, 2).
There are infinitely many solutions.
It is (2, 2).
There is no solution.

Find the perimeter for the irregular polygons below

During one month, a homeowner used 600 units of electricity and 100 units of gas for a total cost of 390. The next month, 400 units of electricity and 250 units of gas were used for a total cost of $326. Find the cost per unit of gas.