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%
since 2500 is exactly the mean (0 std away), look up
P(Z < 0) in your standard table.
Or, just consider the data and pick what seems reasonable in that case.
To find the percentage of light bulbs that have a life less than 2500 hours, we need to calculate the z-score and then use the standard normal distribution table.
The z-score is a measure of how many standard deviations an observation is away from the mean. It is calculated using the formula:
z = (x - μ) / σ
Where:
x = observed value (2500 hours in this case)
μ = mean (2500 hours)
σ = standard deviation (500 hours)
In this case, the z-score would be:
z = (2500 - 2500) / 500 = 0
Since the z-score is 0, we can look up the corresponding value on the standard normal distribution table. The standard normal distribution table gives the cumulative probability (area under the curve) to the left of the given z-score.
Looking up the z-score of 0 in the standard normal distribution table, we find that the cumulative probability is 0.5000.
So, the answer is B) About 50%. Approximately 50% of the light bulbs have a life less than 2500 hours.