Question

The price of a particular brand of jeans has a contractually set retail price averaging mu = $37, but retailers are allowed to charge premiums or run sales at different establishments. Using a sample of size 2 5 ,   t he point estimate of the standard deviation  is  s =   $15 .   Use Excel to answer the following questions:

a.	What is the probability that the sample of jeans will have a mean price less than $40?
b.	What is the probability that the sample of jeans will have a mean price less than $30?
c.	What is the probability that the sample of jeans will have a mean price within $5 of the population mean?

Answer 1

(excel formula are in bold):

mean μ=	37
standard deviation σ=	15.000

sample size       =n=

25

std error=σx̅=σ/√n=

3.0000

a)

from excel:

  probability that the sample of jeans will have a mean price less than $40

norm.dist(40,37,3,true)=0.8413

b)

probability that the sample of jeans will have a mean price less than $30

norm.dist(30,37,3,true)=0.0098

c)

  probability that the sample of jeans will have a mean price within $5 of the population mean:

norm.dist(42,37,3,true)-norm.dist(32,37,3,true)=0.9044