A company makes windows for use in homes and commercial buildings. The standards for glass thickness call for the glass to average

0.400

inch with a standard deviation equal to

0.045

inch. Suppose a random sample of

n=52

windows yields a sample mean of

0.421

inch. Complete parts a and b below.

a. What is the probability of

x0.421

if the windows meet the standards?

Px0.421=enter your response here

(Round to four decimal places as needed.)

b. Based on your answer to part a, what would you conclude about the population of windows? Is it meeting the standards? (A result is unusual if it has a probability less than 0.05.)

The population of windows is/is not

meeting the standards, because a sample of

52

windows with a sample mean of

0.421

inch

would be unusual

would not be unusual

if the population actually had a mean of

0.400

inch and a standard deviation of

0.045

inch.