Question

The lifetime of a certain type of battery is normally distributed with mean value 13 hours and standard deviation 1 hour. There are nine batteries in a package. What lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages? (Round your answer to two decimal places.)

Answer 1

Answer:

13.55 hours

Step-by-step explanation:

given that the  lifetime of a certain type of battery is normally distributed with mean value 13 hours and standard deviation 1 hour.

Sample size=n =9

Sample mean = $\bar X is N(13, 1/3)$

Let c be the  lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages

Then we have $P(X>c) =0.05$

Convert into Z score to get

$P(\frac{x-13}{1/3} >z) = 0.05$

z =1.645 from std normal distribution table

Hence x = $13+\frac{1.645}{3} \\=13+0.548\\=13.548$

Answer is 13.55 hours