Question

In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of

5.45.4​%

with a standard deviation of

6.26.2​%.

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 13.2−13.2​% or lessless	​b) Returns of 5.45.4​% or lessless
​c) Returns between negative 7.0−7.0​% and 17.817.8​%	​d) Returns of lessless than negative 0.8−0.8​%

​a) The expected percentage of returns that are

negative 13.2−13.2​%

or

lessless

is_____?.

​(Type an integer or a​ decimal.)

​b) The expected percentage of returns that are

5.45.4​%

or

lessless

is____?

​(Type an integer or a​ decimal.)

​c) The expected percentage of returns that are between

negative 7.0−7.0​%

and

17.817.8​%

is ____?

​(Type an integer or a​ decimal.)

​d) The expected percentage of returns that are

negative 0.8−0.8​%

or

lessless

is ____?

​(Type an integer or a​ decimal.)

Answer 1

Ans:

​a)-13.2 is 3 standard deviations below the mean

99.7% of the data falls within 3 standard deviations,so 0.3% falls outside,hence half of 0.30% i.e. 0.15% falls below 3 standard deviations.

So,percentage of returns falls below -13.7% is= 0.15%

​b)So,percentage of returns falls below 5.4% is= 50%

(as normal distribution is symmetrical around mean)

​c)-7% and 17.8% are 2 standard deviations below and above the mean respectively.

95% of the data falls within 2 standard deviation of the mean.

percentage of returns falls between -7% and 17.8% is= 95%

​d) -0.8% is one standard deviation below the mean.

68% of the data falls within one standard deviation of the mean,so 32% will fall outside,hence half of 32% i.e. 16% will fall below one standard deviation.

So,Percentage of returns falls below -0.8% is =16%