Question

Trucks in a delivery fleet travel a mean of 100 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 86 and 125 miles in a day. Round your answer to four decimal places.

Answer 1

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = 0.5890 miles

Explanation:

Step(i):-

Given mean of the Population = 100 miles per day

Given standard deviation of the Population = 23 miles per day

Let 'X' be the normal distribution

Let x₁ = 86

`Z_(1) = (x_(1) -mean)/(S.D) = (86-100)/(23) =-0.61`

Let x₂= 86

`Z_(2) = (x_(2) -mean)/(S.D) = (125-100)/(23) = 1.086`

Step(ii):-

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = P(-0.61 ≤ Z≤ 1.08)

= P(Z≤ 1.08) - P(Z≤ -0.61)

= 0.5 +A(1.08) - ( 0.5 - A(-0.61))

= A(1.08) + A(0.61) ( A(-Z)= A(Z)

= 0.3599 + 0.2291

= 0.5890

Conclusion:-

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = 0.5890 miles per day