Question

A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.98mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.70mm. Would this outcome warrant a refund (meaning that it would be unusual)?

Answer 1

0.212 is the probability that a randomly selected tire will have a depth less than 0.70 mm.

Explanation:

We are given the following information in the question:

Mean, μ = 0.98 mm

Standard Deviation, σ = 0.35 mm

We are given that the distribution of tire tread is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

a) P(depth less than 0.70 mm)

P(x < 0.70)

`P( x < 0.70) = P( z < \displaystyle(0.70 - 0.98)/(0.35)) = P(z < -0.8)`

Calculating from normal z table, we have:

`P(z<-0.8) = 0.212`

`P(x < 0.70) = 0.212 = 21.2\%`

Thus, this event is not unusual and will not warrant a refund.