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Answer:
Probability that a set of tires wears out before 20,000 miles is 0.1151.
Step-by-step explanation:
We are given that a tire manufacturer warranties its tires to last at least 20,000 miles or "you get a new set of tires." In its past experience, a set of these tires last on average 26,000 miles with S.D. 5,000 miles. Assume that the wear is normally distributed.
<em>Let X = wearing of tires</em>
So, X ~ N()
Now, the z score probability distribution is given by;
Z = ~ N(0,1)
where, = average lasting of tires = 26,000 miles
= standard deviation = 5,000 miles
So, probability that a set of tires wears out before 20,000 miles is given by = P(X < 20,000 miles)
P(X < 20,000) = P( <
) = P(Z < -1.2) = 1 - P(Z
1.2)
= 1 - 0.88493 = 0.1151
Therefore, probability that a set of tires wears out before 20,000 miles is 0.1151.