# The mean undergraduate cost fo

The mean undergraduate cost for tuition, fees, room, and boardfor four-year institutions was $26,489 for a recent academic year.Suppose that that LaTeX: \sigmaσ =$3204 and that 36 four-yearinstitutions are randomly selected. Find the probability that thesample mean cost for these 36 schools is

a) Less than $25,000 P(x(bar) < 25000)= , Calcuator part Answer= , round your answer to 4 decimal places b) Greater than$26,000 P(x(bar) > 26000)= , Calcuatorpart

c) Between $23,000 and$27,600

P( 23000<x(bar)< 27600)=  , Calcuator part

This is a normal distribution question with

Sample size (n) = 36

Since we know that

a)

P(x < 25000.0)=?

The z-score at x = 25000.0 is,

z = -2.7884

This implies that

b)

P(x > 26000.0)=?

The z-score at x = 26000.0 is,

z = -0.9157

This implies that

P(x > 26000.0) = P(z > -0.9157) = 1 -0.1799121325150559

c)

P(23000.0 < x < 27600.0)=?

This implies that

P(23000.0 < x < 27600.0) = P(-6.5337 < z < 2.0805) =P(Z < 2.0805) – P(Z < -6.5337)

P(23000.0 < x < 27600.0) = 0.9812601521824957 -3.208220514753297e-11

PS: you have to refer z score table to find the finalprobabilities.

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