Answer to Question #72729 in Statistics and Probability for chloe

Question

the annual salaries of employees in a large company are approximately normally distributed with mean of 162,000 and standard deviation of $100,000. what percent of people earn between $140,000 and $180,000

Answer 1

Let X be the random variable of a salary of employee (in $), X ~ N(μ,σ^2).
Then
Z=(X-μ)/σ~N(0,1)
P(140000<X<180000)=P((140000-162000)/100000<Z<(180000-162000)/100000)
=P(-0.22<Z<0.18)
=Φ(0.18)-Φ(-0.22)
=0.5714-0.4129
=0.1585