Question

A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years ("Appliance life expectancy," 2013). The life of a dishwasher is normally distributed. Suppose you are a manufacturer and you take a sample of 10 dishwashers that you made. a.) TRUE or FALSE: The random variable is defined as the sum of dishwasher life expectancies in the sample. b.) For a sample of size 10, state the mean of the sample mean. c.) For a sample of size 10, state the standard deviation of the sample mean (the "standard error of the mean"). d.) Suppose a sample of size 10 is taken. Find the probability that the sample mean dishwasher life expectancy is less than 11 years.

Answer 1

Solution:

Given that,

   = 12 years

= 1.25 years

n = 10

So,

a ) True

= 12

b ) =  ( / )

= (1.25 /10 )

c )  = 0.3953

d ) p (< 11)

= p (-  / ) < ( 11 - 12 / 0.3953)

= p ( z < - 1 / 0.3953 )

= p ( z < - 2.53)

Using z table

= 0.0057

Probability = 0.0057