Solve the problem.
-If the life, in years, of a television set is normally distributed with a mean of 30 years and a standard deviation of 5 years, what should be the guarantee period if the company wants less than $3 \%$ of the television sets to fail while under warranty?
A) Less than 16.25 years
B) Less than 39.4 years
C) More than 20.6 years
D) Less than 20.6 years

Question

Quizplus · Accepted Answer

To find the guarantee period, we need to find the value below which 3% of the television sets will fail. This corresponds to the 3rd percentile of a normal distribution with a mean of 30 years and a standard deviation of 5 years. Using the z-score table, a z-score of approximately -1.88 corresponds to the 3rd percentile. The formula for z-score is $ z = \frac{X - \mu}{\sigma} $, where $ X $ is the value we need to find, $ \mu = 30 $, and $ \sigma = 5 $. Solving for $ X $, we get $ X = \mu + z \cdot \sigma = 30 + (-1.88) \cdot 5 = 20.6 $ years. Therefore, the guarantee period should be less than 20.6 years.

Solve the Problem 3%3 \%3% Of the Television Sets to Fail While Under Warranty? A)

Solve the Problem $3 \%$ Of the Television Sets to Fail While Under Warranty?
A)