Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7 years, and standard deviation of 1.6 years.

If you randomly purchase one item, what is the probability it will last longer than 11 years?

Answer 1

Solution:

     Given: a manufacturer knows that their items have a normally distributed lifespan with mean = 7 years and a standard deviation = 1.6 years.

That is: X follows Normal distribution ( )

We have to find:

P( an item will last longer than 11 years ) =..........?

That is:

P( X > 11) =.........?

Thus find z score for x = 11

Thus we get:

P(X > 11 ) = P( Z > 2.50)

P(X > 11 ) = 1 - P( Z < 2.50)

( We do 1 - P( Z< 2.50) Since table gives only P( Z< z values) )

Now to get: P( Z < 2.50) look in z table for z = 2.5 and 0.00 and find corresponding area.

Thus we get: P( Z < 2.50) = 0.9938

P(X > 11 ) = 1 - P( Z < 2.50)

P(X > 11 ) = 1 - 0.9938

P(X > 11 ) = 0.0062

Thus the probability that an item will last longer than 11 years is 0.0062