Answer to Question #218035 in Statistics and Probability for Yaw

Question

The weekly wages of employees of Volta gold are normally distributed about a mean of $1,250 with a standard deviation of $120. Find the probability of an employee having a weekly wages lying
1) between $1,320 and $970
2) under $1,400
3) over $1,240

Answer 1

1) $P(970<X<1320)=P(\frac{970-1250}{120}<Z<\frac{1320-1250}{120})=P(-2.33<Z<0.58)=$

$=P(Z<0.58)-P(Z<-2.33)=0.7091.$

2) $P(X<1400)=P(Z<\frac{1400-1250}{120})=P(Z<1.25)=0.8944.$

3) $P(X>1240)=P(Z>\frac{1240-1250}{120})=P(Z>-0.08)-1P(Z<-0.08)=0.5319.$