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 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.
If you post YOUR answer, we'll be glad to check it.
What does the difference in standard deviations tell you?
I hope this helps.
To determine which statement is true, we need to compare the average life and the dispersion (or variability) of the tire life for Supplier A and Supplier B.
The average life of the tires is the same for both suppliers, given as 60,000 miles. This means that statement B, which claims that Supplier A's tires have a longer life on average, is not true.
To compare the dispersion of the tire life, we need to consider the standard deviation. The standard deviation measures how spread out the values are around the average. A smaller standard deviation indicates less variability in the data.
Supplier A's tires have a standard deviation of 10,000 miles, while Supplier B's tires have a standard deviation of 2,000 miles. This means that the dispersion of Supplier B's tire life is less than the dispersion of Supplier A's tire life. Thus, statement D, which states that the dispersion of Supplier A's tire life is less than Supplier B's, is not true.
Therefore, the correct statement is C. The life of Supplier B's tires is more predictable than the life of Supplier A's tires, as it has a smaller standard deviation, indicating less variability in the tire life.