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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