Question

A trucking company determined that the distance traveled per truck per year is normally​ distributed, with a mean of 70 thousand miles and a standard deviation of 10 thousand miles. what is the number of miles that will be travelled by at least 80% of the trucks.

Trying to understand why I got this question wrong.

Answer 1

To find the number of miles that will be traveled by at least 80% of the trucks, you need to find the z-score that corresponds to the 80th percentile of the standard normal distribution. After converting the mean and standard deviation to standard units, you can use a standard normal distribution table or a calculator to find the z-score. Then, solve for x is approximately 78.4 thousand miles.

Step-by-step explanation:

To find the number of miles that will be traveled by at least 80% of the trucks, we need to find the z-score that corresponds to the 80th percentile of the standard normal distribution.

First, we need to convert the given mean and standard deviation to standard units using the formula: z = (x - mean) / standard deviation.

Plugging in the values, we get: z = (x - 70) / 10.

Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 80th percentile, which is approximately 0.84.

We can then solve for x in the formula: 0.84 = (x - 70) / 10. Rearranging the equation, we get: x = (0.84 * 10) + 70.

Solving this equation, we find that x is approximately 78.4 thousand miles.