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.
C is the only true statement.
Well, it seems like we're talking about tires here. I must say, I'm not exactly a "tire"-rific expert, but I'll do my best to provide a humorous answer!
Now, let's break down these options:
A. The two distributions of tire life are the same.
Well, since the standard deviations are different, it suggests that the distributions are different. So, I'm afraid A doesn't seem to be the right choice here. Looks like it's not a "tire"-emendous option.
B. On average, Supplier A's tires have a longer life than Supplier B's tires.
Ah, so Supplier A's tires last longer on average? Well, that's "tire"-rific for them! We all want a little extra "mile"-age in our lives, don't we? So, B could be a possible answer worth "tire"-ing out.
C. The life of Supplier B's tires is more predictable than the life of Supplier A's tires.
Well, since Supplier B's standard deviation is considerably smaller, it indicates that the tire life is less variable. So, it seems like Supplier B is more "tire"-ribly predictable, unlike my joke-telling skills!
D. The dispersion of Supplier A's tire life is less than the dispersion of Supplier B's tire life.
Ah, dispersion, the measure of how spread out the data is. Interestingly, Supplier A's standard deviation is larger than Supplier B's, suggesting that the tire life is more dispersed with Supplier A. So, it seems like D might be "tire"-ly accurate!
So, after analyzing these options, it seems like the correct answer here is:
D. The dispersion of Supplier A's tire life is less than the dispersion of Supplier B's tire life.
Hope that helps, and remember, when it comes to tires, always tread carefully!
To determine which statement is true, let's analyze the given information:
Supplier A's tires:
- Average life: 60,000 miles
- Standard deviation: 10,000 miles
Supplier B's tires:
- Average life: 60,000 miles
- Standard deviation: 2,000 miles
A. The two distributions of tire life are the same: This statement is not true as their standard deviations are different, indicating that the distributions of tire life are not the same.
B. On average, Supplier A's tires have a longer life than Supplier B's tires: This statement is not true, as both suppliers have the same average life of 60,000 miles.
C. The life of Supplier B's tires is more predictable than the life of Supplier A's tires: This statement is true. The lower standard deviation of Supplier B's tires (2,000 miles) compared to Supplier A's tires (10,000 miles) indicates that the tire life of Supplier B is more consistent and predictable.
D. The dispersion of Supplier A's tire life is less than the dispersion of Supplier B's tire life: This statement is not true. The standard deviation of Supplier A's tires (10,000 miles) is higher than Supplier B's (2,000 miles), which means there is more variability in the tire life of Supplier A compared to Supplier B.
Therefore, the correct answer is C. The life of Supplier B's tires is more predictable than the life of Supplier A's tires.
To determine which statement is true, we need to compare the average life and the dispersion of the tire life for Supplier A and Supplier B.
Statement A, "The two distributions of tire life are the same," cannot be concluded based on the given information. We need to compare the average life and dispersion to draw a conclusion about the similarity of the distributions.
Statement B, "On average, Supplier A's tires have a longer life than Supplier B's tires," cannot be determined based on the given information. We need to compare the average life of the tires to make a conclusion about their comparative lengths.
Statement C, "The life of Supplier B's tires is more predictable than the life of Supplier A's tires," can be inferred based on the standard deviations given. A smaller standard deviation indicates less dispersion and more predictability. Since Supplier B has a standard deviation of 2,000 miles, compared to Supplier A's 10,000 miles, we can conclude that the life of Supplier B's tires is more predictable.
Statement D, "The dispersion of Supplier A's tire life is less than the dispersion of Supplier B's tire life," cannot be inferred based on the given information. To compare the dispersion, we need to directly compare the standard deviations.
Therefore, the correct answer is C. The life of Supplier B's tires is more predictable than the life of Supplier A's tires.