Question

According to Money, in the year prior to March 2018, the average return for firms of an index was 13.1%. Assume that the standard deviation of returns was 1.2%. If a random sample of 36 companies from the index is selected, what is the probability that their average return for this period will be between 13% and 14%?

Answer 1

To find the probability that the average return for the selected companies will be between 13% and 14%, we use the z-score formula and the standard normal distribution table. The probability is approximately 0.3053.

Step-by-step explanation:

To find the probability that the average return for the selected 36 companies will be between 13% and 14%, we need to use the z-score formula and the standard normal distribution table.

First, we calculate the z-scores for 13% and 14%:

z-score for 13%:

z = (13 - 13.1) / 1.2 = -0.0833

z-score for 14%:

z = (14 - 13.1) / 1.2 = 0.75

Next, we use the standard normal distribution table to find the corresponding probabilities:

Probability of z-score -0.0833:

Lookup the z-score -0.08 and find the corresponding probability, which is approximately 0.4681.

Probability of z-score 0.75:

Lookup the z-score 0.75 and find the corresponding probability, which is approximately 0.7734.

Finally, we subtract the probability of the lower z-score from the probability of the higher z-score:

0.7734 - 0.4681 = 0.3053.

Therefore, the probability that the average return for the selected 36 companies will be between 13% and 14% is approximately 0.3053.