The life span of a battery is normally distributed, with a mean of 2100 hours an

Question

The life span of a battery is normally distributed, with a mean of 2100 hours and a standard deviation of 50 hours. What percent of batteries have a life span that is more than 2160 hours? Would it be unusual for a battery to have a life span that is more than 2160 hours? Explain your reasoning. What percent of batteries have a life span that is more than 2160 hours? Approximately % of batteries have a life span that is more than 2160 hours. (Round to two decimal places as needed.) Would it be unusual for a battery to have a life span that is more than 2160 hours? Explain your reasoning OA tis unusual for a battery to have a life span that is more than 2160 hours because the z-score is within 2 standard deviations of the mean. O B. t is unusual for a battery to have a life span that is more than 2160 hours because the z-score is not within 2 standard deviations of the mean ° C- It is not unusual for a battery to have a life span that is more than 2160 hours because the z-score is within 2 standard deviations of the mean. 0 D. It is not unusual for a battery to have a life span that is more than 2160 hours because the z-score is not within 2 standard deviations of the mean.

Explanation / Answer

Mean = 2100 hours

Standard deviation = 50 hours

P(life span more than 2160 hours) = P(X > 2160)

= 1 - P(X < 2160)

= 1 - P(Z < (2160 - mean)/standard deviation)

= 1 - P(Z < (2160 - 2100)/50)

= 1 - P(Z < 1.2)

= 1 - 0.8849

= 0.1151

= 11.51%

C. It is not unusual for a battery to have a life span mpre than 2160 hours because the z score is within 2 standard deviations of the mean.

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