Question

Question 1 (1 point)

Suppose that a sample of size 60 is drawn from a population with mean 88 and standard deviation 61 . Find the value of , the mean of the distribution of sample means.

Wrtie only a number as your answer.

Your Answer:

Question 2 (1 point)

Suppose that a sample of size 68 is drawn from a population with mean 64 and standard deviation 46 . Find the value of , the standard deviation of the distribution of sample means.

Write only a number as your answer. Round to two decimal places (for example: 8.21).

Your Answer:

Question 3 (1 point)

Suppose that the weight of male babies less than 2 months old is normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds. A sample of 36 babies is selected. What is the probability that the average weight of the sample is less than 11.40 pounds?

Write only a number as your answer. Round to 4 decimal places (for example 0.0048). Do not write as a percentage.

Your Answer:

Question 4 (1 point)

Electricity bills in a certain city have mean $ 111.57 . Assume the bills are normally distributed with standard deviation $ 15.50 . A sample of 69 bills was selected for an audit. Find the 36 percentile for the sample mean.

Write only a number as your answer. Round to two decimal places (for example: 42.81). Do not write any units.

Your Answer:

Question 5 (0.5 points)

A college admissions officer takes a simple random sample of 95 entering freshmen and computes their mean mathematics SAT score to be 463. Assume the population standard deviation is 125. What is the lower bound of the 99% confidence interval?

Round your answer to the nearest integer. Write only a number as your answer.

Your Answer:

Question 6 (0.5 points)

Efficiency experts study the processes used to manufacture items in order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of three holes. In a sample of 65 clamps, the mean time to complete this step was 51.8 seconds. Assume that the population standard deviation is 7 seconds. What is the lower bound of the 98% confidence interval?

Round your answer to one decimal place (for example: 41.9). Write only a number as your answer.

Your Answer:

Answer 1

Solution:

1) The mean of the distribution of sample means = 88

2) The standard deviation of the distribution of sample means = 5.58

=> sx = s/sqrt(n) = 46/sqrt(68) = 5.5783

3) Given that μ = 11.5, σ = 2.7, X = 11.40, n = 36

P(X < 11.40) = P((X-μ)/(σ/sqrt(n)) < (11.40-11.5)/(2.7/sqrt(36)))
= P(Z < -0.2222)
= 0.4129

4) Given μ = 111.57, σ = 15.50, n = 69
  
36 percentile Z = 0.3585, σx = σ/sqrt(n) = 15.50/sqrt(69)

X = μx - Z*σx = 111.57 - (0.3585*15.50/sqrt(69)) = 110.90

5) Given that x = 463, σ = 125, n = 95, 99% Confidence level for Z = 2.576

the lower bound of the 99% confidence interval = X - Z*σ/sqrt(n)
= 463 - 2.576*125/sqrt(95)
= 429.963
= 430
6) Given that x = 51.8, σ = 7, n = 65, 98% Confidence interval Z = 2.33

The lower bound of the 98% confidence interval = 51.8 - 2.33*7/sqrt(65) = 49.776 = 49.8