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% and17.817.8% |
d) Returns of
lessless thannegative 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.)
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%
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