Question

The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a mean of 60,000 miles and a standard deviation of 4,000 miles. Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is between 57,000 and 63,000 miles?

Answer 1

Given,

= 60000 , = 4000

Using central limit theorem,

P( < x) = P(Z < ( x - ) / ( / sqrt(n) ) )

So

P(57000 < < 63000 ) = P( < 63000 ) - P( < 57000 )

= P(Z < ( 63000 - 60000) / ( 4000 / sqrt(4) ) ) - P(Z < ( 57000 - 60000) / ( 4000 / sqrt(4) ) )

= P(Z < 1.5) - P(Z < -1.5)

= 0.9332 - 0.0668

= 0.8664