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.

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

rational decision making is a multi-step process for making choices between alternatives. the process of rational decision making favors logic, objectivity, and analysis over subjectivity and insight. the word “rational” in this context does not mean sane or clear-headed as it does in the colloquial sense.

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