1. Given a normal distribution with , = 50 and a = 5, if you select a sample of n = 100, what is the probability that X is:

a. less than 47?

b. between 47 and 49.5?

c. above 51.1 ?

d. There is a 35% chance that X is above what value?

2. a business intelligence company that produces tools and reports for the apps and digital goods industry, smartphone owners are using an average of 30 apps per month. Assume that number of apps used per month by smartphone owners

is normally distributed and that the standard deviation is 5. If you select a random sample of 25 smartphone owners,

a. what is the probability that the sample mean is between 29 and 31?

b. what is the probability that the sample mean is between 28 and 32?

c. If you select a random sample of 100 smartphone owners, what is the probability that the sample mean is between 29 and 31?

d. Explain the difference in the results of (a) and (c).

3. The following data represent the yes or no (Y or N) responses from a sample of 40 college students to the question "Do you currently own shares in any stocks?"

N N Y N N Y N Y N Y N N Y N Y Y N N N Y

N Y N N N N Y N N Y Y N N N Y N N Y N N

a. Determine the sample proportion, p, of college students who own shares of stock.

b. If the population proportion is 0.30, determine the standard error of the proportion.

4. An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inches. The lower and upper e r specification limits under which the ball bearing can operate are 0.74 inches (lower) and 0.76 inches (upper). Past experience has indicated that the actual diameter of the ball bearings is approximately normally distributed, with a mean of 0.753 inches and a standard deviation of 0.004 in ch. If you select a random sample of 25 ball bearings, what is the probability that the sample mean is

a. between the target and the population on a mean of 0. 753?

b. between the low e r specification limit and the target?

c. greater than the upper specification on limit?

d. less than the lower specification limit?

e. The probability is 93% that the sample mean diameter will be greater than what value?

5. The fill amount of bottles of a so f t drink is normally distributed, with a mean of2.0 liters and a standard deviation of0.05 liters. If you select a random sample of 2 5 bottles, what is the probability that the sample mean will be:

a. between 1.99 and 2.0 liters?

b. below 1.98 liters?

c. greater than 2.0 I liters?

d. The probability is 99% that the sample mean amount of soft drink will be at least how much?

e. The probability is 99% that the sample mean amount of soft drink will be between which two values (symmetrically distributed around the mean)?