Trucks in a delivery fleet travel a mean of 100 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 166 and 177 miles in a day. Round your answer to four decimal places.

Answer: the probability that a truck drives between 166 and 177 miles in a day is 0.0187

Step-by-step explanation:

Since mileage of trucks per day is distributed normally, we would apply the formula for normal distribution which is expressed as

z = (x - µ) / σ

Where

x = mileage of truck

µ = mean mileage

σ = standard deviation

From the information given,

µ = 100 miles per day

σ = 37 miles miles per day

The probability that a truck drives between 166 and 177 miles in a day is expressed as

P (166 ≤ x ≤ 177)

For x = 166

z = (166 - 100) / 37 = 1.78

Looking at the normal distribution table, the probability corresponding to the z score is 0.9625

For x = 177

z = (177 - 100) / 37 = 2.08

Looking at the normal distribution table, the probability corresponding to the z score is 0.9812

Therefore,

P (166 ≤ x ≤ 177) = 0.9812 - 0.9625 = 0.0187