Question

Assuming mileages obtained by a certain brand of tire are uniformly distributed with a mean of 25,000 miles and a range of 10,000 miles

(a) What are the lower and upper limits of tire mileages?

(b) What is the probability that a tire will last 26,000 miles or more?

Answer 1

Let X be a random variable denoting the mileages obtained by a certain brand of tire.

Let X~Uniform(a, b).

a)

The mean of X is given to be 25000 miles. We know that, E(X) =(a+b) /2. Thus, here (a+b) =50000.

The range of X is 10000 miles, i.e., (b-a) =10000.

Therefore, b=30000, a=20000.

Therefore, X~Uniform(20000, 30000). Thus, the PDF of X is,

f(x) =1/1000, 20000<X<30000.

Thus, lower and upper limits of tire mileages are 20000 miles and 30000 miles respectively.

b)

Now the probability that a tire will last 26000 miles or more is,

P(X26000)

=

=(30000-26000) /10000

=0.4

Thus, the required probability is=0.4.