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.)

hours

Answer 1

Given that,

mean = = 13

standard deviation = =1

Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05

= P(Z < z ) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.65 ) = 0.95  

z = 1.65 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.65 *1+13

x= 14.65=15 rounded