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.)

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 =

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

Convert into Z score to get

z =1.645 from std normal distribution table

Hence x =

Answer is 13.55 hours

look a the sides they are perpendicular