Answer:
To answer this question, we need to use the properties of a normal distribution. So, the answer is b. 10,200
Explanation:
The mean and standard deviation serve as the defining characteristics of a normal distribution, a form of probability distribution. The average tire lifespan in this situation is 50,000 miles, with a standard variation of 5,000 miles.
The number of tires that should last between 45,000 and 55,000 miles, or the region under the normal distribution curve between these two figures, is what we're looking for. The conventional normal table or a calculator using the inverse cumulative probability function can be used to find this region.
We can standardize the values by using the standard normal table, which is (X-mean)/standard deviation.
(45,000-50,000) / 5,000 = -1
(55,000-50,000) / 5,000 = 1
The area between -1 and 1 standard deviation from the mean is about 0.6826, which is the proportion of the tires that are expected to last between 45,000 and 55,000 miles.
To find the number of tires, we can multiply the proportion by the sample size (15,000)
0.6826 * 15,000 = 10,200
So, the answer is b. 10,200