Question

The mean cost for college textbooks per semester is $636 with a standard deviation of $117. If all possible random samples of size 49 are taken from this population, determine the following:

a) name of the Sampling Distribution?

b) mean and standard error of the sampling distribution of the mean (use the correct name and symbol for each)?

c) percent of sample means that are less than $600?

d) probability that sample means fall between $500 and $800?

e) Below which sample mean can we expect to find the lowest 25% of all the sample means?

Answer 1

SolutionA:

n=49

n>30 large sample

As n>30 follows normal distribution.

name of the Sampling Distribution=normal distribution

Solutionb:

mean of the samplling distributin=xbar=636

standard error of sampling distribution=s=sigma/srqrt(n)

=117/sqrt(49)

=117/7

s=16.71429

c) percent of sample means that are less than $600?

P(xbar<600)

z=x-mean/stderror

=600-636/16.71429

=-36/16.71429

=-2.15385

P(Z<2.15385)=1-P(Z<-2.15385)

=1-0.9842

=0.0158*100

ANSWER:1.58%

Solutiond:

P(500<Xbar<800)

P(500-636/16.71429<Z<800-636/16.71429)

P(-8.14<Z<9.81)=1

ANSWER:1