Question

According to Glassdoor, the average base salary for a brand manager in Bethlehem, PA, is $88,592 and the average base salary for a brand manager in New York City, NY is $97,417. Assume that salaries are normally distributed, the standard deviation for brand managers in Bethlehem is $19,000, and the standard deviation for brand managers in New York is $21,000.

1. What is the probability that a brand manager in Bethlehem has a base salary in excess of $100,000? Answer
2. What is the probability that a brand manager in New York has a base salary in excess of $100,000? Answer
3. What is the probability that a brand manager in New York has a base salary of less than $75,000? Answer
4. How much would a brand manager in New York have to make in order to have a higher salary than 99% of the brand managers in Bethlehem (do not use neither the dollar sign nor coma in your answer)? $

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	88592
std deviation   =σ=	19000.00

probability =P(X>100000)=P(Z>(100000-88592)/19000)=P(Z>0.6)=1-P(Z<0.6)=1-0.7257=0.2743

b)

here mean=       μ=	97417
std deviation   =σ=	21000.00

probability =P(X>100000)=P(Z>(100000-97417)/21000)=P(Z>0.12)=1-P(Z<0.12)=1-0.5478=0.4522

c)

probability =P(X<75000)=(Z<(75000-97417)/21000)=P(Z<-1.07)=0.1423

d)

for 99th percentile critical value of z=		2.33
therefore corresponding value=mean+z*std deviation=88592+2.33*19000=			132862.00