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 =
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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