The mean life of a certain brand of auto batteries is 44 months with a standard deviation of 3 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 35 to 53 months. Round your answer to one decimal place.

99.7%

Step-by-step explanation:

Using the z score formula

z-score is z = (x-μ) / σ

where:

x = raw score

μ = population mean

σ = population standard deviation.

a) for x = raw score = 35

μ = population mean = 44

σ = population standard deviation = 3

z = (35 - 44) / 3

z = - 9/3

z = - 3

b) for x = raw score = 53

μ = population mean = 44

σ = population standard deviation = 3

z = (53 - 44) / 3

z = 9/3

z = 3

We would use the standard normal distribution table to find their probabilities

P (Z<=-3) = 0.0013499

P (Z<=+3) = 0.99865

So P (-3<=Z<=3) = 0.99865 - 0.0013499 = 0.9973

Converting to percentage = 0.9973 * 100 = 99.73%

Therefore, the percentage of auto batteries of this brand that have a life of 35 to 53 months to one decimal place is 99.7%