Question

Please answer all three parts and show all work. Thank you!

A cheap tire is said to have its tire wear (how long it lasts (in thousands of miles as N(30,12) (that is normal with μ =30, σ =12)

Find the probability that

1. A tire lasts more than 35,000 miles

2. A tire lasts less than 28,000 miles

3. A tire lasts between 31,000 and 36,000 miles

Answer 1

Find z score for normal distribution using the formula:

z = (x - μ) / σ

1. A tire lasts more than 35,000 miles

z = (35000-30000) / 12000 = 0.42

P(Z > 0.42) = 0.3372

2. A tire lasts less than 28,000 miles

z =(28000-30000)/12000 = -0.17

P(< -0.17) = 0.4325

3. A tire lasts between 31,000 and 36,000 miles

Z =(31000-30000)/12000 = 0.08

Z =(36000-30000)/12000 = 0.50

P(0.08 < Z < 0.50) = 0.1596