The battery life of a new rechargeable battery is normally distributed with a mean of 1,450 hours and a standard deviation of 8.5 hours. If one of these new rechargeable batteries is selected at random, what is the probability that its battery life will be between 1,440 and 1,465 hours? Round to the nearest whole number.(1 point)

Question

Responses

98%
98%

68%
68%

95%
95%

48%

Answer 1

68%

To find the probability that the battery life will be between 1,440 and 1,465 hours, we need to calculate the z-scores for both values and find the area under the curve between these two z-scores.

z-score for 1,440 hours:
(z1 = (1,440 - 1,450) / 8.5 = -1.176)

z-score for 1,465 hours:
(z2 = (1,465 - 1,450) / 8.5 = 1.765)

Using a z-table or calculator, we can find the area between -1.176 and 1.765 which corresponds to approximately 68%.