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Question 1

E270 Statistics Fall 2020 Quiz 3 2 questions worth 100 points each

Question 1

Motorola used the normal distribution to determine the probability of defects and

the number of defects expected in a production process. Assume the production

process produces items with a mean weight of 10 ounces. Calculate the probability

of a defect and the expected number of defects for a 1000-unit production run in the

following situations.

a) The process standard deviation is .15, and the process control at plus or minus one standard deviation.

Units with weights of less than 9.85 ounces or greater than 10.15 ounces will be classified as defects.

b) Through process design improvements, the process standard deviation can be reduced to .05.

Assume the process control remains the same with weights less than 9.85 ounces or greater than

10.15 ounces being classified as defects.

c) What is the advantage of reducing the process variation, thereby causing process control limits

to be at a greater number of standard deviations from the mean.

The New York Times reported that 17.2 million new cars and light trucks were sold in

the United States in 2017, the the U.S. Environmental Protection Agency projects the

average efficiency of thesee vehicles to be 25.2 miles per gallon. Assume that the

population standard deviation for these automobiles is σ = 6.

a) What is the probability a sample of 70,000 new cars and light trucks sold in the

United States in 2017 will provide a sample mean miles per gallon that is within

.05 miles per gallon of the population mean of 25.2?

b) What is the probability a sample of 70,000 new cars and light trucks sold in the

United States in 2017 will provide a sample mean miles per gallon that is within

.01 miles per gallon of the population mean of 25.2?

c) What is the probability a sample of 90,000 new cars and light trucks sold in the

United States in 2017 will provide a sample mean miles per gallon that is within

.01 miles per gallon of the population mean of 25.2?

Comment on the differences between your answers to part b and c.

d) Suppose that the mean miles per gallon for a sample of 70,000 new cars and light trucks

sold in the United States in 2017 differs from the population mean µ by more than one gallon.

How would you interpret this result?