A) A group of mutual funds earned varying annual rates of return in the last yea

Question

A) A group of mutual funds earned varying annual rates of return in the last year. These rates of return are normally distributed with a mean of 8% and a standard deviation of 15%.

One mutual fund in this group managed to earn a rate of return that was double that of this group's average that year. This performance would put the fund in the top X% of those funds in that year.

Calculate X%. Give your answer to 1 decimal place.

X%= ? %

B) A teacher gives her class a particular examination on mathematics at the end of each year. The results are normally distributed with a mean test score of 63 and a standard deviation of 8.

The teacher has told the class that students with a test score in the top 2.5% will win a special prize.

Calculate the test score above which 2.5% of all test scores lie. Give your answer to 1 decimal place.

Test score = ?

Explanation / Answer

A)as for normal distribution ; z score =(X-mean)/std deviaiton

double of average return =8*2 =16

hence P(X>16) =P(Z>(16-8)/15)=P(Z>0.5333)=0.297 ~ 29.7%

hence X% =29.7%

B)

for top 2.5% ; z score =1.96

hence test score =mean +z*std deviation =63+1.96*8=78.7

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