Answer:
a) [tex] \mu -\sigma =48-3=45[/tex]
[tex] \mu -\sigma =48+3=51[/tex]
68% of all batteries will have a life between 45 months and 51 months.
b) [tex] \mu -\sigma =48-2*3=42[/tex]
[tex] \mu -\sigma =48+2*3=54[/tex]
95% of all batteries will have a life between 42 months and 54 months.
Step-by-step explanation:
For this case we know the following info given for the life of a Brand Q car battery:
[tex]\mu = 48, \sigma =3[/tex]
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:
[tex] \mu -\sigma =48-3=45[/tex]
[tex] \mu -\sigma =48+3=51[/tex]
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:
[tex] \mu -\sigma =48-2*3=42[/tex]
[tex] \mu -\sigma =48+2*3=54[/tex]
95% of all batteries will have a life between 42 months and 54 months.
