In the last quarter of 2007, a group of 64 mutual funds had a mean return of 3.3

Question

In the last quarter of 2007, a group of 64 mutual funds had a mean return of 3.3% with a standard deviation of 4.5%. If the 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. Please show steps

1) Returns of -10.2 or less.

Whats the expected percentage of returns that are -10.2% or less?

2) Returns of 3.3% or more

Whats the expected percentage of returns that are 3.3% or more?

3) Returns between 1.2 and 7.8%

Whats the expected percentage of returns that are between 1.2 and 7.8%?

4) returns of more than 12.3%

Expected percentage of returns more than 12.3%?

Explanation / Answer

1) P(X < -10.2)

= P(z < (-10.2 - 3.3)/4.5)

= P(z < -3)

= 0.0015

2) P(X > 3.3)

= P(z > (3.3 - 3.3)/4.5)

= P(z > 0)

= 0.5

3) P(-1.2 < X < 7.8)

= P((-1.2 - 3.3)/4.5 < z < (7.8 - 3.3)/4.5)

= P(-1 < z < 1)

= 0.68

4) P(X > 12.3)

= P(z > (12.3 - 3.3)/4.5)

= P(z > 2)

= 0.025

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