Question

1. According to the National Association of Colleges and Employers, the average starting salary for new college graduates in health science in $51,541. The average starting salary for new college graduates in business is $53,901. (National Association of Colleges and Employers website, January 5, 2015). Assume that starting salaries are normally distributed and that the standard deviation for starting salaries for new college graduated in health sciences is $11,000, Assume that the standard deviation for starting salaries for new graduates in business is $15,000.

1. What is the probability that a new college graduate in business will earn a starting salary is at least $65,000?
2. What is the probability that a new college graduate in health sciences will earn a starting salary is at least $65,000?
3. What is the probability that a new college graduate in health sciences will earn a starting salary is less than $40,000?
4. How much would a new college graduate in business have to earn in order tp have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences?

Answer 1

for normal distribution z score =(X-μ)/σ

a)

probability =P(X>65000)=P(Z>(65000-53901)/15000)=P(Z>0.74)=1-P(Z<0.74)=1-0.7704=0.2296

b)

probability =P(X>65000)=P(Z>(65000-51541)/11000)=P(Z>1.22)=1-P(Z<1.22)=1-0.8888=0.1112

c)

probability =P(X<40000)=(Z<(40000-51541)/11000)=P(Z<-1.05)=0.1469

d)

for 99th percentile critical value of z=

2.33

therefore corresponding value=mean+z*std deviation=53901+2.33*11000 =

77171.00