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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%

Verified Answer :

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%