Question 359712: Please help me:0
A car battery is known by the manufacturer to last 65 months with a standard deviation of 4.5 months.
a. If the manufacturer guarantees them for five years (60 months), what percentage of them will they have to replace?
b. If the manufacturer does not want to replace more than 4% of the batteries, for how many months should they guarantee them (round to the nearest whole month)?
thanks you :)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A car battery is known by the manufacturer to last 65 months with a standard deviation of 4.5 months.
a. If the manufacturer guarantees them for five years (60 months), what percentage of them will they have to replace?
---
z(60) = (60-65)/4.5 = -1.1111
--
%(x < 60) = P(z < -1.1111) = 13.33%
---------------------------------------------
b. If the manufacturer does not want to replace more than 4% of the batteries, for how many months should they guarantee them (round to the nearest whole month)?
---
Find the z-value with a right tail of 4%.
invNorm(0.96) = 1.7507
---
Find the corresponding raw score value:
x = zs+u
x = 1.7507*4.5+65
x = 72.88 months
----
He should guarantee them for 72 months or 6 years.
==================================================
Cheers,
Stan H.
|
|
|
