Solve the problem.
-If the life, in months, of a certain type of car battery is normally distributed with a mean of 76 months and a standard deviation of 10 months, what should be the guarantee period if the company wants less than $5 \%$ of the batteries to fail while under warranty?
A) Less than 50.2 months
B) Less than 12.54 months
C) Less than 92.5 months
D) Less than 59.5 months

Question

Quizplus · Accepted Answer

To find the guarantee period, we need to find the z-score that corresponds to the 5th percentile of a standard normal distribution, which is approximately -1.645. Using the formula $X = \mu + z\sigma$, where $\mu = 76$ and $\sigma = 10$, we calculate $X = 76 + (-1.645)(10) = 59.55$. Thus, the guarantee period should be less than 59.5 months.

Solve the Problem 5%5 \%5% Of the Batteries to Fail While Under Warranty? A) Less

Solve the Problem $5 \%$ Of the Batteries to Fail While Under Warranty?
A) Less