If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, approximately what percentage of light bulbs has a life of more than 3000 hours?
A. About 84%
B. About 68%
C. About 32%
D. About 16%
Answer B
I got .1587, which matches 16% or D
Did you take 1 - ...., since it asked for "above" ?
Disagree. "More than" includes everything below the mean.
Agree.
PsyDag do you agree with Reiny or the answer i have
I misread the Question, so your answer
To solve this question, you will need to use the concept of standard deviation and the normal distribution.
Step 1: Calculate the z-score
The z-score measures how many standard deviations an observation is from the mean. It can be calculated using the formula:
z = (x - μ) / σ
Where:
- x is the value we are interested in (3000 hours)
- μ is the mean of the distribution (2500 hours)
- σ is the standard deviation of the distribution (500 hours)
Plugging in the values, we get:
z = (3000 - 2500) / 500
z = 500 / 500
z = 1
Step 2: Find the percentage using the standard normal distribution table
The standard normal distribution table gives you the percentage of values below a given z-score. Since we are interested in values above 3000 hours, we need to calculate the percentage of values below 3000 hours first, and then subtract it from 100%.
Looking up the z-score of 1 in the standard normal distribution table, you will find that it corresponds to approximately 84%.
Step 3: Subtract the percentage from 100%
Since we want to find the percentage of values above 3000 hours, we subtract the 84% from 100%.
100% - 84% = 16%
Therefore, approximately 16% of light bulbs have a life of more than 3000 hours.
So the answer is D. About 16%.