Question

A mutual fund company promises that their clients earn an average of 10% on investments they recommend. The returns have a population standard deviation of 2%. In a sample of 25 investments, you find that the average return is 8.90% with a standard deviation of 4%.  

1. Find the probability of a single return being less than 8.90%. Use clear calculations

2. Find the probability of the average of 25 returns being less than 8.90%. Use clear calculations.

1. Identify which of the curves given below will represent the population of individual values (in part a) and which curve represents the sampling distribution of the sample mean (in part b), Mark off the mean income of the population. Show graphically, by labeling the curves (population of single values and sampling distribution) and shading the appropriate areas under the curves, that the probability of a single return being less than 8.90% is more than the probability of the average of 25 returns being less than 8.90%.

Answer 1

Part a.

Part b.