Question

PLEASE WRITE CLEARLY
After deducting the grants based on needs, the average cost to attend the University of Southern California (USC) is $27175. (US News and World report America Best Colleges,2009 ed). Assume the population standard deviation is $7400. Suppose that a random sample of 60 USC students will be taken from this population.

a.What is the value of the standard error of the mean? (1pt)

b.What is the probability that the sample mean will be more than $27175?(1pt)

c.What is the probability that the sample mean will be within $1000 of the population mean?(1pt)

Answer 1

a)

standard error of the mean σx̅=population standard deviation/√n =7400/√60=955.3359
b)

since sample size is greater than 30 , we can use normal approximation from central limit theorem:

for normal distribution z score =(X-μ)/σx

here mean=       μ=

27175

std error=σx̅=σ/√n=

955.3359

  probability that the sample mean will be more than $27175:

probability =P(X>27175)=P(Z>(27175-27175)/955.336)=P(Z>0)=1-P(Z<0)=1-0.5=0.5

c)

  probability that the sample mean will be within $1000 of the population mean:

probability =P(26175<X<28175)=P((26175-27175)/955.336)<Z<(28175-27175)/955.336)=P(-1.05<Z<1.05)=0.8531-0.1469=0.7062