Question

The mean life of a certain brand of auto batteries is 51 months with a standard deviation of 6 months. Assume that the lives of all auto batteries of this brand have a bell-shaped distribution. Using the empirical rule, find the percentage of auto batteries of this brand that have a life of

a. 33 to 69 months: %

b. 45 to 57 months: %

Answer 1

The empirical rule is a statistical rule which states that for a normal distribution, almost all data will fall within three standard deviations of the mean. Broken down, the empirical rule shows that 68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the distribution's average.

a. Now we need to find

As distribution is normal we can convert x to z

So as per empirical rule answer here is 99.7%

b. Here we need to find

As distribution is normal we can convert x to z

So as per empirical rule answer here is 68%