Question 1) Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 36.6 and 3.7 mpg, respectively. Use Table 1.

a. What is the probability that a randomly selected passenger car gets more than 37 mpg?

b. What is the probability that the average mpg of three randomly selected passenger cars is more than 37 mpg?

c. If three passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 37 mpg?

Question 2) Consider a population proportion p = 0.27.

a-1. Calculate the standard error for the sampling distribution of the sample proportion when n = 17 and n = 65?

a-2. Is the sampling distribution of the sample proportion approximately normal with n = 17 and n = 65?

b. Can you use the normal approximation to calculate the probability that the sample proportion is between 0.25 and 0.27 for both sample sizes?

Question 3) A random sample of size n = 225 is taken from a population with population proportion P = 0.55. Use Table 1.

a. Calculate the expected value and the standard error for the sampling distribution of the sample proportion.

b. What is the probability that the sample proportion is between 0.50 and 0.60?

c. What is the probability that the sample proportion is less than 0.50?

Question 4) American workers are increasingly planning to delay retirement (US News & World Report, June 30, 2010). According to a Pew Research Center comprehensive survey, 35% of employed adults of age 62 and older say they have pushed back their retirement date. Use Table 1.

a. What is the probability that in a sample of 100 employed adults of age 62 and older, more than 40% have pushed back their retirement date?

b. What is the probability that in a sample of 200 employed adults of age 62 and older, more than 40% have pushed back their retirement date?

Attachment:- Table 1.rar