If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Multiply by 100.
However, it would be easier if you realized that the mean, median and mode of a normal distribution were the same value.
To determine the percentage of light bulbs that have a life less than 2500 hours, we need to calculate the area under the normal distribution curve to the left of 2500 hours.
First, let's standardize the value 2500. We can do this by subtracting the mean and then dividing by the standard deviation.
Standardized value (Z-score) = (2500 - 2500) / 500 = 0
Now, we can use a standard normal distribution table or a statistical software to find the cumulative probability associated with a Z-score of 0. This represents the percentage of values below 2500 hours.
Using a standard normal distribution table, we find that the cumulative probability for a Z-score of 0 is 0.5. This means that 50% of light bulbs have a life less than 2500 hours.
Therefore, the answer is 50%.