Question

he amount of pressure created from a air compressor spray is normally distributed with a mean of 10,000 pounds per square inch (PSI) and standard deviation of 800 PSI.

(1) For a random sample of n=4 sprays, what is the probability that the sample mean will be at least 10,200 PSI?
(2) For a random sample of n=4 sprays, what is the probability that the sample mean will be less than 9,900 PSI?

Answer 1

Solution: It is given that the amount of pressure created from an air compressor spray is normally distributed with a mean of 10,000 pounds per square inch (PSI) and standard deviation of 800 (PSI). Therefore, we have:

(1) For a random sample of n=4 sprays, what is the probability that the sample mean will be at least 10,200 PSI?

Answer: We are required to find:

Now using the z-score formula, we have:

Now using the standard normal table, we have:

Therefore, the probability that the sample mean will be at least 10,200 PSI is 0.3085

(2) For a random sample of n=4 sprays, what is the probability that the sample mean will be less than 9,900 PSI?

Answer: We are required to find:

Now using the z-score formula, we have:

Now using the standard normal table, we have:

Therefore, the probability that the sample mean will be less than 9,900 PSI is 0.4013