Question 1102278: 01. The life span of a battery ins normally distributed with mean 30 months ans standard deviation 5 months
a) what percentage of batteries will have a life span less than 35 months
b) what is the probability that the life span is less than 40 months
Answer by Lightning_Fast(78)   (Show Source):
You can put this solution on YOUR website! Use the equation.
z-score = (mean - actual value) / (standard deviation)
We know the mean is 30 months and the standard deviation is 5 months, so plug that into the equation.
z-score = (30 - actual value) / (5)
Now, you are given the actual value for a.) and b.). So plug in 35 and 40 into the equation given just above. Simplify and you will get a z-score.
Now use a z-score chart your teacher gave you or find one on the internet: http://image.tutornext.com/cms/files/Z%20score%20table1.JPG
For example, if you get a z-score of -1.00, go under the 'z' or 'z-score' column and look for -1. Once you find it, move to the right until your decimal matches the one listed above. Since the decimal for -1.00 is .00, you want to be under the 0.00 column and in the -1 row.
The value you get, for example, 0.1587. gives you the probability of getting that actual value you plugged in or less than the actual value you plugged in. If you want to convert that to a percent, multiply by 100 and add a % sign.
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