Question

In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 4.3​% with a standard deviation of 7.7​%. If a normal model can be used to model​ them, what percent of the funds would you expect to be in each​ region? Use the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more precisely. Be sure to draw a picture first. ​a) Returns of negative 11.1​% or less ​b) Returns of 4.3​% or more ​c) Returns between negative 18.8​% and 27.4​% ​d) Returns of more than 12.0​% ​a) The expected percentage of returns that are negative 11.1​% or less is nothing​%. ​(Type an integer or a​ decimal.)

Answer 1

(A) Return of negative 11.1% means 2 standard deviation below the mean

using empirical rule, area below 2 standard or more is 0.0235+0.0015 = 0.025

(B) Return of 4.3% or more means values above the mean

using empirical rule, area above mean = 0.50

(C) -18.8% is 3 standard deviation below the mean and 27.4% is 3 standard deviation above the mean

using empirical rule, we know that 99.7% or 0.997 of values found between 3 standard deviation below and above the mean

So, required probability is 0.997