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?
A. About 25%
B. About 50%
C. About 75%
D. About 68%
Answer B
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 for the Z score. Multiply by 100.
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 for the Z score. Multiply by 100.
However, if you realize that the mean and median are the same in a normal distribution, you won't need to go through all that work.
Sorry, I didn't see your answer. You are right.
To find the percentage of light bulbs with a life less than 2500 hours, we can use the concept of the standard normal distribution.
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. To convert the given distribution (mean = 2500 hours, standard deviation = 500 hours) into the standard normal distribution, we need to calculate the z-score.
The z-score formula is given by:
z = (x - mean) / standard deviation
In this case, x represents the value we want to find the probability for (2500 hours), the mean is 2500 hours, and the standard deviation is 500 hours.
Calculating the z-score:
z = (2500 - 2500) / 500
z = 0
Now, we can use a standard normal distribution table or a statistical calculator to find the area under the curve to the left of z = 0, which represents the percentage of light bulbs with a life less than 2500 hours.
The area to the left of z = 0 is 0.5000 or 50%.
Therefore, the correct answer is B. About 50% of light bulbs have a life less than 2500 hours.