The quarterly returns for a group of 51 mutual funds are well modeled by a Norma

Question

The quarterly returns for a group of 51 mutual funds are well modeled by a Normal model with a mean of 6.3?% and a standard deviation of 1.2?%. Use the? 68-95-99.7 Rule to find the cutoff values that would separate the following percentages of? funds, rather than using technology to find the exact values.

?a) the highest 50?%

?b) the highest 16?%

?c) the lowest 2.5?% ?

d) the middle 68?%

?a) Select the correct choice and fill in any answer boxes in your choice below. ?(Round to one decimal place as? needed.)

A. x less than or equals --------%

B. x greater than or equals -------%

C. --------?%less than or equals x less than or equals --------%

?b) Select the correct choice and fill in any answer boxes in your choice below. ?(Round to one decimal place as? needed.)

A. x less than or equals ------?%

B. x greater than or equals ------?%

C. -------%less than or equals x less than or equals --------?% ?

c) Select the correct choice and fill in any answer boxes in your choice below. ?(Round to one decimal place as? needed.)

A. x less than or equals ------?%

B. x greater than or equals -----?%

C. -------?%less than or equals x less than or equals ------?%

?d) Select the correct choice and fill in any answer boxes in your choice below. ?(Round to one decimal place as? needed.)

A. x less than or equals -------%

B. x greater than or equals -------?%

C. -------?% less than or equals x less than or equals ----------?%

Explanation / Answer

Ans:

Given that

mean=6.3

standard deviation=1.2%

a)Highest 50% means that

P(Z>=z)=0.5

z=0

For,highest 50% x should greater than or equal to 6.3%

b)Highest 16%

P(Z>=z)=0.16

z cut off value=1

so,x=6.3+0.9944*1.2=7.5%

Greater than or equal to 7.5%

c)the lowest 2.5%

cut off value,z=-2

x=6.3-2*1.2=3.9%

less than or equal to 3.9%

d)middle 68%

middle 68% lies within one standard deviation of the mean

lower cut off=6.3-1.2=5.1%

upper cut off=6.3+1.2=7.5%

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