Question

A manufacturer produces tires. The lifetime of the tires is normally distributed with a mean of 25,000 miles and a standard deviation of 2,000 miles. What percent of the tires can be expected to last between 25,000 miles and 28,500 miles?

Answer 1

Solution :

Given that ,

mean = = 25000

standard deviation = = 2000

P(25000< x < 28500) = P[(25000-25000) / 2000< (x - ) / < (28500-25000) /2000 )]

= P( 0< Z <1.75 )

= P(Z < 1.75) - P(Z <0 )

Using z table   

= 0.9599 - 0.5

= 0.4599

=45.99%