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

In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 5.5​% 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 17.6​% or less ​

b) Returns of 5.5​% or less ​

c) Returns between negative 9.9​% and 20.9​%

​d) Returns of less than negative 2.2​%.

According to 68-95-99.7 rule, 68%, 95% and 99.7% of data values lie within 1, 2 and 3 standard deviations of mean respectively.

a) P(returns of negative 17.6​% or less) = 0.0015

b) P(returns of 5.5​% or less) = 0.5

c) P(returns between negative 9.9​% and 20.9​) = 0.95

d) P(returns of less than negative 2.2​%) = 0.0015 + 0.0235 + 0.1350 = 0.16

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