Question

A purchasing agent for a trucking company is shopping for replacement tires for their trucks from two suppliers. The suppliers’ prices are the same. However, Supplier A’s tires have an average life of 60,000 miles with a standard deviation of 10,000 miles. Supplier B’s tires have an average life of 60,000 miles with a standard deviation of 2,000 miles. Which of the following statements is true?A. the two distributions of tire life are the same.

B. on average, Supplier A's tires have a longer life than Supplier B's tires.
C. the life of Supplier B's tires is more predictable than the life of Supplier A's tires.
D. the dispersion of Supplier A's tire life is less than the dispersion of Supplier B's tire life.

Answer 1

Answer: C. The life of Supplier B's tires is more predictable than the life of Supplier A's tires.

Step-by-step explanation: This conclusion is based on the information provided. The standard deviation is a measure of the spread or variability of a data set. In this case, Supplier B's tires have a much lower standard deviation (2,000 miles) compared to Supplier A's tires (10,000 miles). A lower standard deviation indicates that the data points (in this case, tire lifespans) are closer to the mean (average), making the distribution more predictable and less variable.

Therefore, Supplier B's tires are more predictable in terms of their lifespan compared to Supplier A's tires, which have a wider range of variability in their lifespan.

Answer 2

C. the life of Supplier B's tires is more predictable than the life of Supplier A's tires.

Explanation:

A: The distributions have the same mean, but different standard deviation. They are not the same distribution.

B: The distributions have the same mean, which means on average the tire lifetimes are the same from both suppliers.

C: A smaller standard deviation means values tend to be closer to the mean, hence more predictable. Supplier B's tires have a more predictable life.

D: "Dispersion" is another way to describe the measure provided by standard deviation. Supplier B's tires have a lower tire life dispersion.