Question

The mean life of a Brand Q car battery is 48 months. The standard deviation is 3

months.
Part A: 68% of all batteries will have a life between
months and
months.
Part B: 95% of all batteries will have a life between
months and
months.

Answer 1

a)
`\mu -\sigma =48-3=45`

`\mu -\sigma =48+3=51`

68% of all batteries will have a life between 45 months and 51 months.

b)
`\mu -\sigma =48-2*3=42`

`\mu -\sigma =48+2*3=54`

95% of all batteries will have a life between 42 months and 54 months.

Explanation:

For this case we know the following info given for the life of a Brand Q car battery:

`\mu = 48, \sigma =3`

Part a

For this case we can use the empirical rule and we know that we have 68% of the values within one deviation from the mean, and if we find the limits we got:

`\mu -\sigma =48-3=45`

`\mu -\sigma =48+3=51`

68% of all batteries will have a life between 45 months and 51 months.

Part b

From the empirical rule and we know that we have 95% of the values within one deviation from the mean, and if we find the limits we got:

`\mu -\sigma =48-2*3=42`

`\mu -\sigma =48+2*3=54`

95% of all batteries will have a life between 42 months and 54 months.