Question

In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 2.1​% with a standard deviation of 6.5​%. 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 4.4​% or less ​b) Returns of 2.1​% or less ​c) Returns between negative 10.9​% and 15.1​% ​d) Returns of more than 21.6​% ​a) The expected percentage of returns that are negative 4.4​% or less is nothing​ %. ​(Type an integer or a​ decimal.) ​b) The expected percentage of returns that are 2.1​% or less is nothing​ %. ​(Type an integer or a​ decimal.) ​c) The expected percentage of returns that are between negative 10.9​% and 15.1​% is nothing​ %. ​(Type an integer or a​ decimal.) ​d) The expected percentage of returns that are 21.6​% or more is nothing​ %. ​(Type an integer or a​ decimal.)

Answer 1

Using mean = 2.1% and standard deviation = 6.5%

Curve for the data is

​a) Returns of negative 4.4​% or less

Using given curve, -4.4% is 1 standard deviation below the mean. By 68-95-99.7 rule, 16% of data fall below one standard deviation to the left of mean. Hence, The expected percentage of returns that are negative 4.4​% or less is 16%

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​b) Returns of 2.1​% or less

Using given curve, -2.1% is the mean. By 68-95-99.7 rule, 50% of data fall below the mean value. Hence, The expected percentage of returns that are 2.1​% or less is 50%

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​c) Returns between negative 10.9​% and 15.1​% ​

Using given curve, -10.9% is 2 standard deviation below the mean and 15.1% is 2 standard deviations above the mean. By 68-95-99.7 rule, 95% of data fall between two standard deviation to the left and right the of mean. Hence, The expected percentage of returns that are between negative 10.9​% and 15.1​% is 95 %

d) Returns of more than 21.6​%

Using given curve, 21.6% is 3 standard deviation above the mean. By 68-95-99.7 rule, 0.15% of data fall above three standard deviation to the right of mean. Hence, The expected percentage of returns that are 21.6% or more is 0.15%

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