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A tire company measures the tread on newly-produced tires and finds that they are normallydistributed with a mean depth of 0.98mm and a standard deviation of 0.35mm. Find theprobability that a randomly selected tire will have a depth less than 0.50mm. Would thisoutcome warrant a refund (meaning that it would be unusual)?Homework Help:4VA. Calculating normal probabilities (2:18)4DA. Description of normal distribution, area, and probabilities, definition of unusual events(DOCX)O Probability of 0.09 and would warrant a refund© Probability of 0.91 and would warrant a refundO Probability of 0.09 and would not warrant a refundProbability of 0.91 and would not warrant a refund

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Solution

Mean = 0.98mm

Standard Deviation = 0.35mm

Let X be a random variable

We want to find

p(X<0.5mm)

[tex]\begin{gathered} p(X<0.5)=p(z<\frac{0.5-0.98}{0.35}) \\ p(X<0.5)=p(z<-1.37) \\ p(X<0.5)=0.085343 \\ p(X<0.5)=0.09\text{ (to two decimal places)} \end{gathered}[/tex]

The answer is

[tex]p(X<0.5)=0.09\text{ (to two decimal places)}[/tex]

Probability of 0.09 and would warrant a refund

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