Please answer ASAP

Question

a manufacturer of automobile batteries claims that average length of life for its grade A battery is 70 months, suppose the standard deviation of the life length is known to be 10 months. a) approximately what percentage of the manufacturer's grade A battery will last more than 90 months or less than 50 months?

b) suppose your battery lasts for 45 months, what could you infer about the manufacturer's claims?? thanks

Answer 1

To answer this question, you will need to know about the normal distribution curve and the percentages of data which fall a certain number of standard deviations away from the mean (aka - average).  If you don't have this information handy (or memorized), you can look up a normal distribution curve on Google - check out the images.

 

A)  If the mean length of life for the battery is 70 months with a standard deviation (SD) of 10 months, then you need to calculate how many standard deviations 90 months and 50 months are away from the mean.  You can use this formula:

Value - Mean   =    90 - 70    =     20    = 2 SD

       SD                    10               10

 

If you do the same with 50, you will find that the question is asking you what percentage of the manufacturer's grade-A batteries fall higher than 2 SDs away from the mean or fewer than -2 SDs.  According to the normal distribution curve, 2.3% of the batteries will be higher than 2 SDs away from the mean and 2.3% of the batteries will be lower than -2 SDs from the mean.  By adding the two 2.3%s, we can find that the answer is 4.6%.

 

B)  Find how many SDs away from the mean 45 months is using the above formula.  You should get -2.5 SD.  Now look at the normal distribution curve. and see what the percentage of getting a battery that lasts at -2.5 SDs below the average battery.  (In this situation, there is a 0.6% chance that a battery will last 45 months, -2.5 SDs.  That means that there is a 99.4% chance that the manufacturer's claim is incorrect.)

 

Hope this helps!

 

~Patty