Question

Slader records show that the average life expectancy of a pair of shoes is 2.2 years with astandard deviation of 1.7 years. A manufacturer gaurantees that shoes lasting less than a year are replaced for free. For every 1000 pairs sold how many pairs should the manufacturer expect to replaces free? Assume a normal distributiom.

Answer 1

For every 1000 pairs sold, the manufacturer expect to replace 239 pairs for free.

Explanation:

Given:

Mean (μ) = 2.2, Standard deviation(S.D) (σ) = 1.7 years and x = 1 (1 year)

Let's find the Z score.

Z =
`(x - mean)/(S.D)`

Now plug in the given values in the above formula, we get

Z =
`(1 - 2.2)/(1.7) = -0.71`

Now we have to use the z-score table.

The z-score for 0.71 is 0.2611

Since it z is negative, so we subtract 0.2611 from 0.5000

0.5000 - 0.2611 = 0.2389

Percentage = 0.2389 × 100 = 23.89%

To find replaces for 1000 pairs, we need to multiply 23.89% by 1000

=
`(23.89)/(100) .1000 = 238.9`

= 239

The cannot be in decimal, when we round off to the nearest whole, we get

239