The salaries of pediatric physicians are approximately normally distributed. If

Susan Munoz

Susan Munoz

Answered question

2021-11-14

The salaries of pediatric physicians are approximately normally distributed. If 25 percent of these physicians earn below 180, 000 and 25 percent earn above 320,000, what fraction earn (a) below 250,000; (b) between 260,00 and 300,000?

Answer & Explanation

Daniel Williams

Daniel Williams

Beginner2021-11-15Added 14 answers

Let X be a random variable that represents the salary of some pediatric physician, XN(μ,σ2), and with Z=Xμσ standard normal we have:
0.25=P(X<180)=P(Z<180μσ)P(Z<0.675)=0.25
0.25=P(X>320)=P(Z<320μσ)P(Z>0.675)=0.25
And from that:
180μσ=0.675180μ=0.675σ
320μσ=0.675320μ=0.675σ
If we add both expressions together, we will get 180μ+320μ=0500=2myμ=250 and given that
σ=700.675=103.7
a) P(X<250)=P(Z<250250103.7)=P(Z<0)=Φ(0)=0.5
b) P(260<X<300)=P(260250103.7<Z<300250103.7)
=P(10103.7<Z<50103.7)
=P(0.096<Z<0.482)=P(Z<0.482)P(Z<0.096)
=Φ(0.482)Φ(0.096)=0.15

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?