SOLUTION: I need help... The shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 3.9 years and a standard deviation of 0.3 years

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Question 867588: I need help...
The shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 3.9 years and a standard deviation of 0.3 years. What is the probability that a randomly chosen battery will last fewer than 3.2 years?
Thanks!
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
First you need the standard z-score

z = (x - mu)/sigma

z = (3.2 - 3.9)/0.3

z = -2.33333333333333

z = -2.33 round to 2 decimal places

Now we use a table like this one here to find the area under the standard normal distribution curve that is to the left of z = -2.33

According to the table, the area is roughly 0.0099 (look in the row that starts with -2.3 and then look in the column that starts with 0.03, where they intersect is at the cell with the number 0.0099 in it)

So the approximate answer is 0.0099

If you need a more accurate answer, use a calculator that can compute normal cdfs