Answer to Question #229078 in Statistics and Probability for pranty

Question

The mean hourly pay rate for financial managers in the East North Central region is 30$ and the variance is 9$^2 (Bureau of Labor Statistics). Assume that pay rates are normally distributed. 

a) Write the chance function of the above normal random variable.

b) What is the probability that a financial manager earns between 30$ and 35$ per hour? 

c) For a randomly selected financial manager, what is the probability the manager earned more than 20$ per hour?

Answer 1

$N(30,9)$

a. Chance Function

$f(x)=\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}, -\infin<x<\infin$

$f(x)=\frac{1}{3 \sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-30}{3})^2}, -\infin<x<\infin$

b. $P(30<x<35)$

$P(30<x<35)=P(\frac{30-30}{3}<Z<\frac{35-30}{3})$

$=P(0<Z<0.6)$

$=P(Z<0.6)-P(Z<0)$

$=0.7257-0.5$

$=0.2257$

c. $P(x>20)$

$P(x>20)=P(z>\frac{20-30}{3})$

$=1-P(Z<-3.333)$

$=1-0.004$

$=0.9996$