Question

Brand x batteries have a mean life span of 102 hours, with a standard deviation of 6.8 hours. brand y batteries have a mean life span of 100 hours, with a standard deviation of 1.4 hours. complete each of the sentences.
about 68% of brand x’s batteries have a lifespan between ____ and ____ hours. about 68% of brand y’s batteries have a lifespan between _____ and _____ hours. the life span of brand _____’s battery is more likely to be consistently close to the mean.

Answer 1

Answer:

about 68% of brand x’s batteries have a lifespan between 95.2 hours and 108.8 hours. about 68% of brand y’s batteries have a lifespan between 98.6 hours and 101.4 hours. the life span of brand y’s battery is more likely to be consistently close to the mean.

Explanation:

According to the empirical rule (68–95–99.7 rule) for a normal distribution, 68% of the data falls within the first standard deviation (μ ± σ).

Given for brand x, mean (μ) = 102 hours and standard deviation (σ) = 6.8 hours.

first standard deviation (μ ± σ) = 102 ± 6.8 = (95.2, 108.8)

about 68% of brand x’s batteries have a lifespan between 95.2 hours and 108.8 hours.

Given for brand y, mean (μ) = 100 hours and standard deviation (σ) = 1.4 hours.

first standard deviation (μ ± σ) = 100 ± 1.4 = (98.6, 101.4)

about 68% of brand x’s batteries have a lifespan between 98.6 hours and 101.4 hours.

Since the standard deviation of brand y is smaller than that of brand x, brand y battery is more likely to be consistently close to the mean