Question

Rucks in a delivery fleet travel a mean of 130

miles per day with a standard deviation of 37
miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 174
and 196
miles in a day. Round your answer to four decimal places.


please help

Answer 1

To solve this problem, we need to standardize the values using the z-score formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

First, we need to find the z-score for the lower bound:

z1 = (174 - 130) / 37 = 1.1892

Next, we need to find the z-score for the upper bound:

z2 = (196 - 130) / 37 = 1.7838

Now we need to find the probability of the z-score falling between z1 and z2. We can use a standard normal distribution table or a calculator to find this probability. Using a calculator, we get:

P(1.1892 < z < 1.7838) = 0.0966

Rounding to four decimal places, we get the final answer:

The probability that a truck drives between 174 and 196 miles in a day is approximately 0.0966.