Question

A compact disc is designed to last an average of 4 years with a standard deviation of 0.8 years.

What is the probability that a CD will last less than 3 years?

1.11%

10.56%

86.65%

100%

Answer 1

10.56%

Explanation:

We are given A compact disc is designed to last an average of 4 years with a standard deviation of 0.8 years.

We are supposed to find What is the probability that a CD will last less than 3 years

We will use z-score formula:

`z=(\bar x- \mu)/(\sigma)`

`\bar x =3`

`\mu = 4`

`\sigma =0.8`

Substitute the values in the formula

`z=(3- 4)/(0.8)`

`z=-1.25`

Now refer the z score table

So, the value of -1.25 is 0.1056 =
`(0.1056)/(100) \% = 10.56\%`

Thus , the probability that a CD will last less than 3 years is 10.56%