Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. what is the probability that a tire lasts between 54,000 and 66,000 miles?

To solve for the P (54,000≤x≤66000) we proceed as follows:

z-score = (x-μ) / σ

μ-60000

σ-4000

thus:

when x=66,000

z-score = (66000-60000) / 4000=1.5

P (z≤1.5) = 0.9332

when x=54000

z = (54000-60000) / 4000

z=-1.5

P (z≤-1.5) = 0.0668

thus

P (54,000≤x≤66000)

=P (z≤1.5) - P (z≤-1.5)

=0.9332-0.0668

=0.8664

Answer: 0.8664