Answer:
Step-by-step explanation:
If we are looking for the probability that the battery lasts between 7 and 8 years, we find the z-score for the probability that it lasts less than 8 years, and then subtract from it the z-score for the probability that it lasts less than 7 years. This subtraction will give you what's left: the span in between 7 and 8 years. To find the z-score:
[tex]z=\frac{x_i-\mu}{\sigma}[/tex] Therefore,
P(x < 8) has a z-score of
[tex]z=\frac{8-5}{1.2}=1.667[/tex] The p-value that accompanies this z-score is .99379 (which translates to 99.379% of the data falling below 8 years) and
P(x < 7) has a z-score of
[tex]z=\frac{7-5}{1.2}=2.5[/tex] The p-value that accompanies this z-score is .95224 (which translates to 95.224% of the data falling below 7 years).
Subtract the p-value of 2.5 from the p-value of 1.667 to get
.99379 - .95224 = .04155 = 4.16%, choice A.
