Given that z is a standard normal random variable: a. P(z lessthanorequalto 2.0)

Question

Given that z is a standard normal random variable: a. P(z lessthanorequalto 2.0) b. P(z greaterthanorequalto 2.0) c. P (-1.22 lessthanorequalto z lessthanorequalto 1.45) d. Find the z-value if the area to the left of z is.5000 Extra Credit Question The mean hourly pay rate for financial managers in the East North Central region is exist32.62 and the standard deviation is exist2.32 (Bureau of Labor Statistics). Assume that pay rates are normally distributed. a. What is the probability a financial manager earns between exist30 and exist35 per hour? b. How high must the hourly rate be to put a financial manager in the top 5% with respect to pay?

Explanation / Answer

Ans:1a)P(z<=2)=0.97725

b)P(z>=2)=1-0.97725=0.02275

c)P(-1.22<z<1.45)=P(z<1.45)-P(z<-1.22)=0.926471-0.111232=0.815239

d)P(Z<z)=0.5

z=0

2)a)mean=32.62,std dev=2.32

P(30<x<35)=P(x<35)-P(x<30)

z score for 35

z=(35-32.62)/2.32=1.026

z score for 30

z=(30-32.62)/2.32=-1.129

P(-1.129<z<1.026)=P(z<1.026)-P(z<-1.129)=0.847554-0.129449=0.718105

b)For P(Z<z)=0.95

z=1.645

1.645=(x-32.62)/2.32

x=36.4364

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