Question

The lifetime of a certain type of battery is normally distributed with mean value 10 hours and standard deviation 1 hour. There are four 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 packs

Answer 1

Answer:43.29 hr

Step-by-step explanation:

Given

mean
`\mu =10 hr`

standard deviation
`\sigma =1 hr`

n=4

Total Life time of four batteries
`=4\cdot \mu =4\cdot 10=40 hr`

`P\left [(x-\mu )/((\sigma )/(√(n)))> (x-40)/((1)/(√(4)))\right ]=5%`

`P\left [ z> (x-40)/((1)/(√(4)))\right ]=0.05`

`1-P\left [ z< (x-40)/((1)/(√(4)))\right ]=0.05`

`P\left [ z< (x-40)/((1)/(√(4)))\right ]=0.95`

from z table limiting value of
`z=1.645`

thus
`(x-40)/(2)=1.645`

`x-40=3.29`

`x=43.29`