normal distribution

Question

Laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. Find the probability that a randomly selected light bulb will last between 600 and 750 hours.

Answer 1

The probabilities for normal distributions fall into certain standard amounts based on increments of standard deviations like this:

In this case, one standards deviation below the mean is 750 - 75 or 675. Two standard deviations below the mean would be 750 - 2(75) = 750 - 150 = 600. That is exactly what we are looking for. So we want to know the probabilities that make up the area between -2 and 0 in the graph above (because the mean, or 750, is "0" and two standard deviations, or 600, is "-2").

On the graph, we see that we just need to add 13.6% and 34.1% and when we add them we get 47.7%.

You should have a graph in your notes or textbook like this. Please refer to that because they may round these percentages differently. But, that a randomly selected light bulb will last between 600 and 750 hours is approximately 47.7%