Answer to Question #160374 in Statistics and Probability for Akbar khan

Question #160374

The mean annual cost to attend a college is $44,324. Assume the distribution of  annual costs follows the normal probability distribution and the standard deviation is $4,590.

Ninety percent of all students pay less than what amount?


1
Expert's answer
2021-02-03T03:44:34-0500

Let X=X= the annual cost to attend a college: XN(μ,σ2)X\sim N(\mu, \sigma^2)

Then Z=XμσN(0,1)Z=\dfrac{X-\mu}{\sigma}\sim N(0, 1)

Given μ=$44324,σ=$4590\mu=\$44324, \sigma=\$4590


P(X<x)=P(Z<X443244590)=0.9P(X<x)=P(Z<\dfrac{X-44324}{4590})=0.9

X443244590=1.28155157\dfrac{X-44324}{4590}=1.28155157

X=50206.32X=50206.32

Ninety percent of all students pay less than $50206.32



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