# Probability Density

1. Aug 28, 2010

### kukumaluboy

1. The problem statement, all variables and given/known data

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)

2. Relevant equations

3. The attempt at a solution
Part (i) i can do. Part (ii) dun understand. 5% of all batteries sold? how many are they?

2. Aug 28, 2010

### lanedance

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

3. Aug 28, 2010

### kukumaluboy

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

4. Aug 28, 2010

### 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

5. Aug 28, 2010

### 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

6. Aug 28, 2010

### kukumaluboy

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

7. Aug 28, 2010

### lanedance

ok so in that table you want to find when the probabilty 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