the charge life of a certain ion battery for camcorder is normally distributed with a mean of 90 minutes and standard deviation of 35 minutes.
What is the probability that a battery of this type (random ) last more than 100 minutes on a single charge?
is the answer unusual yes or no
Thank You
OK, this is not hard. The probability the charge will last more than 90 minutes is 50%, by definition, because 90 minutes is the mean charge life and the normal distribution is symmetrical - this means that half of all observations will be above the mean and half below the mean.
So the answer we are looking for is (50-x)%, where x is the probability that the charge will last more than 90 but less than 100 minutes.
Now, we are told that the standard deviation is 35 minutes. So, 100 minutes is 10/35 (in other words 0.286) standard deviations above the mean.
Take a look at the table referenced in the sources. We need the Z-value that corresponds to 0.286. Look at the last two values in the third row down. These correspond to 0.28 and 0.29 standard deviations respectively. To get the value corresponding to 0.286 standard deviations, we interpolate between these two values and we get 0.113 - in other words, 11.3%. This is the probability that the charge life is between 90 and 100 minutes.
So our answer is 50-11.3 which is 38.7%.
Is this unusual? No. What it tells us is that nearly 4 out of 10 batteries will last more than 100 minutes on a single charge. Is this surprising? No. This is because the standard deviation is very large by comparison with the mean (and in that sense this example is rather unusual). Because of this, the extra 10 minutes is really quite close to the mean in statistical terms, so the probability is not much less than 50%.
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