Question

The top-selling Red and Voss tire is rated 60000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 72000 miles and a standard deviation of 4000 miles.

A. What is the probability that the tire wears out before 60000 miles?

Probability =

B. What is the probability that a tire lasts more than 80000 miles?

Probability =

Answer #1

Solution :

Given that ,

mean = = 72000

standard deviation = =4000

P(x <60000 ) = P(( x -) / (60000 - 72000) / 4000)

= P(z < -3)

Using z table

= 0.0013

(B)

P(x > 80000) = 1 - P(x < 80000)

= 1 - P[(x - ) / < (80000 -72000) /4000 ]

= 1 - P(z < 2)

Using z table,

= 1 -0.9772

= 0.0228

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