The major stock market indexes had strong results in a recent year. The mean one-year return for stocks in Index A, a group of very large companies, was 12.5%. The mean one-year return for stocks in Index B, a group of small and medium-sized companies, was 16.5%.

Historically, the one-year returns are approximately normally distributed, the standard deviation in Index A is approximately

20%, and the standard deviation in Index B is approximately 47%.

Complete parts (a) through (f) below.

a. What is the probability that a stock in Index A gained value in this year?

Round to four decimal places as needed

b. What is the probability that a stock in Index A gained 15% or more in this year?

Round to four decimal places as needed

c. What is the probability that a stock in Index A lost 20% or more in this year?

Round to four decimal places as needed

d. What is the probability that a stock in index A lost 25% or more in this year?

Round to four decimal places as needed

e What is the probability that a stock in Index B gained value in this year?

Round to four decimal places as needed

What is the probability that a stock in Index B gained

15% or more in this year?

Round to four decimal places as needed

What is the probability that a stock in Index B lost 20% or more in this year?

Round to four decimal places as needed

What is the probability that a stock in Index B lost

25% or more in this year?

Round to four decimal places as needed

f. Choose the correct answer below.

A. While stocks in Index B have a higher mean one-year return and a higher probability of a large gain of

15% or more than stocks in Index A, due to the greater variation of index B, they also have a higher probability of sustaining large losses of 20%

or more

B. While stocks in Index B have a higher mean one-year return and a higher probability of a gain than stocks in Index A, due to the greater variation of Index B, they also have a higher probability of sustaining large losses of

25% or more.

C. While stocks in Index B have a higher mean one-year return than stocks in Index A, they have a lower probability of a large gain of 15%

or more or a large loss of 20% or more due to their greater variation.

D. While stocks in Index B have a higher mean one-year return and a higher probability of a gain than stocks in Index A, due to the greater variation of Index B, they have a lower probability of a large gain of 15% or more.