Answer to Question #287156 in Statistics and Probability for Julier

Question

Teachers’Salaries The average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680. Find the probability that a randomly selected teacher earns

a. Between $35,000 and $45,000 a year

b. More than $40,000 a year

c. If you were applying for a teaching position and were offered $31,000 a year, how would you feel

Answer 1

a. $P(35000<X<45000)=P(\frac{35000-47750}{5680}<Z<\frac{45000-47750}{5680})=$

$=P(-2.24<Z<-0.48)=P(Z<-0.48)-P(Z<-2.24)=$

$=P(Z<2.24)-P(Z<0.48)=0.3031.$

b. $P(X>40000)=P(Z>\frac{40000-47750}{5680})=P(Z>-1.36)=$

$=P(Z<1.36)=0.9131.$

c. $P(X<31000)=P(Z<\frac{31000-47750}{5680})=P(Z<-2.95)=$

$=1-P(Z<2.95)=0.0016.$

Since this probability is very unusual, you would feel very bad.