Question

In testing a certain kind or truck tire over rugged​ terrain, it is found that 25 ​% of the trucks fail to complete the test run without a blowout. ​(a) Of the next 16 trucks​ tested, how many of them would you expect to have​ blowouts? ​(b) What is the variance of the number of blowouts experienced by the 16 ​trucks? What does that​ mean?

Answer 1

25 ​% of the trucks fail to complete the test run without a blowout

That means P=25% = 0.25             and    n=16

a)

Expected blowouts = n *P = 16 * 0.25 = 4

4 trucks are expected to have blowouts.

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b)

Variance = n* P * (1-P)

=16 * 0.25 * (1-0.25)

=3

Variance = 3

Variance is the average of the squared distances from each point to the mean.

Which means that the expected value of the squared deviation from mean is 3.