Question

The mean life of a certain brand of auto batteries is 44 months with a standard deviation of 2 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 38 to 50 months. Round your answer to one decimal place.

a) 68.3%

b) 95.5%

c) 99.7%

d) 84.1%

Answer 1

To find the percentage of auto batteries of this brand that have a life of 38 to 50 months, we can use the empirical rule. The percentage is approximately 99.7%.

Step-by-step explanation:

To find the percentage of auto batteries of this brand that have a life of 38 to 50 months, we can use the empirical rule. The empirical rule states that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations. Since the mean life is 44 months and the standard deviation is 2 months, we can calculate the range of 38 to 50 months in terms of standard deviations: Lower Bound: (38 - 44) / 2 = -3, Upper Bound:(50 - 44) / 2 = 3. So the lower bound is 3 standard deviations below the mean and the upper bound is 3 standard deviations above the mean. From the empirical rule, we know that approximately 99.7% of the data falls within three standard deviations of the mean. Therefore, the percentage of auto batteries of this brand that have a life of 38 to 50 months is approximately 99.7%.