Answer to Question #289552 in Statistics and Probability for Chappy

Question

The monthly salaries of contract workers in a small Jamaican shipping company are approximately normally distributed with a mean of $60,000 and a standard deviation of $4,000. What percent of people earn less than $55,000?

Answer 1

Let $X=$the monthly salary: $X\sim N(\mu, \sigma^2 ).$

Given $\mu=\$60000, \sigma=\$4000.$

$$P(X<55000)=P(Z<\dfrac{55000-60000}{4000})$$

$$=P(Z<-1.25)=0.10565$$

$10.565\%$