Question

Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 24 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 108 and 153 miles in a day. Round your answer to four decimal places.

Answer 1

Answer:

0.6069

Step-by-step explanation:

Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 24 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 108 and 153 miles in a day. Round your answer to four decimal places.

We solve using z score formula

z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

For x = 108 miles

z = ( 108 - 120)/24

z = -0.5

Probability value from Z-Table:

P(x = 108) = 0.30854

For x = 153 miles

z = (153 - 120) /24

= 1.375

Probability value from Z-Table:

P(x = 153) = 0.91543

The probability that a truck drives between 108 and 153 miles in a day is

P(x = 153) - P( x = 108)

0.91543 - 0.30854

= 0.60689

Approximately = 0.6069