Question
According to the Normal model N(0.067 ,0.017 ) describing mutual fund returns in the 1st quarter...
According to the Normal model N(0.067 ,0.017 ) describing mutual fund returns in the 1st quarter of 2013, determine what percentage of this group of funds you would expect to have the following returns. Complete parts (a) through (d) below. a) Over 6.8%? b) Between 0% and 7.6%? c) More than 1%? d) Less than 0%?
Homework Answers
Answer #1
a) P(X > 0.068)
= P((X - 
)/
> (0.068 - )/)
= P(Z > (0.068 - 0.067)/0.017)
= P(Z > 0.06)
= 1 - P(Z < 0.06)
= 1 - 0.5239
= 0.4761 = 47.61%
b) P(0 < X < 0.076)
= P((0 - )/
< (X - )/
< (0.076 - )/)
= P((0 - 0.067)/0.017 < Z < (0.076 - 0.067)/0.017)
= P(-3.94 < Z < 0.53)
= P(Z < 0.53) - P(Z < -3.94)
= 0.7019 - 0
= 0.7019 = 70.19%
c) P(X > 0.01)
= P((X - )/
> (0.01 - )/)
= P(Z > (0.01 - 0.067)/0.017)
= P(Z > -3.35)
= 1 - P(Z < -3.35)
= 1 - 0.0004
= 0.9996 = 99.96%
d) P(X < 0)
= P((X - )/
< (0 - )/)
= P(Z < (0 - 0.067)/0.017)
= P(Z < -3.94)
= 0.00 = 0%
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