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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)?

Respuesta :

Answer:

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:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

a) P(depth less than 0.70 mm)

P(x < 0.70)

[tex]P( x < 0.70) = P( z < \displaystyle\frac{0.70 - 0.98}{0.35}) = P(z < -0.8)[/tex]

Calculating from normal z table, we have:

[tex]P(z<-0.8) = 0.212[/tex]

[tex]P(x < 0.70) = 0.212 = 21.2\%[/tex]

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

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