Atire 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)?

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

Step-by-step 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:

a) P(depth less than 0.70 mm)

P(x < 0.70)

Calculating from normal z table, we have:

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

In order to solve the problem above, represent the width by x. With this, the length of the rectangular portrait is 1.5x. The perimeter of the rectangle is two times the sum of the length and width. This translates to, 

                                    2 (1.5x + x) = 10 ft, x = 2 ft.

Thus, the length of the rectangular portrait is 3 ft.