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?

Answer 1

The probability of the disk lasting less than 3 years is very high.

Considering that on average it's around 4 years with a standard devaiation of 0.8

M = 4
SD = 0.8

The probability that it will last less than 3 years means that

we have to substract 4 - 0.8 (the difference of 1 standard deviation is 34% of the data and the difference of 2 standard deviations is 14% of the data)

Because it's more than 3 years (3.2) we have to do this again.

3.2 - 0.8

is

2.6 - this is less than 3 years.

Now we see that in order for a disk to last less than 3 years, it has to be 2 standard deviations apart from the mean.

This means that there is a 5% probability of its breaking down.

Answer 2

Given the mean of 4 years
Standard Deviation of 0.8 years

We are looking for the probability of that CD for 3 years.

P = (probability of the CD - mean) / standard deviation
P = (4 - 3) / 0.8
P = 1.25

So the probability is 1.25