Probability Density: Battery Life Homework

[kukumaluboy]

Homework Statement

c. The life of a certain brand of battery is normally distributed with a mean of 4 years and a
standard deviation of 1. 2 years.
i. If a battery is selected at random, what is the probability that it will last for more than 6
years? (5 marks)
ii. How long a warranty period should the manufacturer provide if he is willing to replace
at most 5% of all the batteries sold? (5 marks)

Homework Equations

The Attempt at a Solution

Part (i) i can do. Part (ii) dun understand. 5% of all batteries sold? how many are they?

 

[lanedance]

so a single battery hsould have a 95% probability of lasting the warranty period

 

[kukumaluboy]

So should we do (b - a) in years ?

 

[lanedance]

i would look at the cumulative distribution & pick of the time at 5%

as your pdf is defined in years, I would find the answer in years

 

[kukumaluboy]

I am using this table here
http://www.intmath.com/Counting-probability/z-table.php

Could you show me the working.

Formulae: Z = (X-mean)/standard deviation

Mean is 4 and standard deviation is 1.2.
The answer in my test paper shows 2 years

 

[kukumaluboy]

I tried working from the answer, the Z value have to be -1.65

 

[lanedance]

ok so in that table you want to find when the probability is 0.45 (the othe side of the curve will give you 0.5 probabiliy as it is symmetric)

so reading off P = 0.45, at z=1.65

so 95% of the batteries will have a life greater than
= Mean - 1.65 x SD
= 4yrs - 1.65x1.2 = 4-2.3 = 1.7

which is pretty close to 2