1)A normal population has a mean of 60 and a standard deviation of 12

1)A normal population has a mean of 60 and a standard deviation of 12. You select a random sample of 9. Compute the probability the sample mean is:

a. Greater than 63.

b. Less than 56.

c. Between 56 and 63.

2. A population of unknown shape has a mean of 75. You select a sample of 40. The standard deviation of the sample is 5. Compute the probability the sample mean is:

a. Less than 74.

b. Between 74 and 76.

c. Between 76 and 77.

d. Greater than 77.

3. The mean rent for a one-bedroom apartment in Southern California is $2,200 per month. The distribution of the monthly rents does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 50 one-bedroom apartments and finding the mean to be at least $1,950 per month? The standard deviation of the sample is $250.

So probability is 1 or virtually certain. 

4. According to an IRS study, it takes an average of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. A consumer watchdog agency selects a random sample of 40 taxpayers and finds the standard deviation of the time to prepare, copy, and electronically file form 1040 is 80 minutes.

a. What assumption or assumptions do you need to make about the shape of the population?

b. What is the standard error of the mean?

c. What is the likelihood the sample mean is greater than 320 minutes?

d. What is the likelihood the sample mean is between 320 and 350 minutes?

e. What is the likelihood the sample mean is greater than 350 minutes?