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

Answer:

10.56%

Step-by-step 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:

$z=\frac{\bar x- \mu}{\sigma}$

$\bar x =3$

$\mu = 4$

$\sigma =0.8$

Substitute the values in the formula

$z=\frac{3- 4}{0.8}$

$z=-1.25$

Now refer the z score table

So, the value of -1.25 is 0.1056 = $\frac{0.1056}{100} \% = 10.56\%$

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