The previous answer is wrong. I\'ll appreciate if answered correctly. Thank you

Question

The previous answer is wrong. I'll appreciate if answered correctly. Thank you

A Salary Survey for University graduates (less than 5 years of work experience) reveals that the Bachelor of Science graduates’ annual average salary is $70,439 with a standard deviation of $11,080; the Master of Science graduates earn an average of $81,672 per year with a standard deviation of $9,080.

Assume the data follows a Gaussian distribution. Answer the following questions:

a) What is the percentage of BS graduates who earn more than the average of MS graduates?

b) What is the percentage of BS graduates who earn more than the 90% of MS graduates?

Explanation / Answer

a) percentage of BS graduates who earn more than the average of MS graduates

=P(X>81672) =P(Z>(81672-70439)/11080)=P(Z>1.0138)=0.1553 ~ 15.53%

b)zscore for 90th percentie z =1.2816

for 90th percentile of MS graduates earning =81672+1.2816*9080=93308.49

hence percentage of BS graduates who earn more than the 90% of MS graduates

=P(X>93308.49)=P(Z>(93308.49-70439)/11080)=P(Z>2.0640)=0.0195 ~ 1.95%

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