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?
well, 3000 is 1 std above the mean. So, check your Z table for the area of the tail above Z=1.
Or, play around at
http://davidmlane.com/hyperstat/z_table.html
To find the percentage of light bulbs that have a life of more than 3000 hours, we need to calculate the area under the normal curve to the right of 3000 hours.
Here's how you can do it step by step:
Step 1: Standardize the value 3000 hours using the z-score formula:
z = (x - μ) / σ
Where:
x = 3000 hours (the value we want to find the percentage for)
μ = mean = 2500 hours
σ = standard deviation = 500 hours
Substituting the values:
z = (3000 - 2500) / 500
z = 500 / 500
z = 1
So, the standardized value is z = 1.
Step 2: Look up the z-score in the standard normal distribution table (also known as the z-table) to find the corresponding percentage.
The standard normal distribution table provides the area under the curve to the left of various z-scores. Since we need the area to the right of z = 1, we can use the fact that the total area under the curve is 1 (or 100%).
Using the standard normal distribution table, the area to the left of z = 1 is approximately 0.8413. Therefore, the area to the right of z = 1 (which represents light bulbs that last more than 3000 hours) is:
1 - 0.8413 = 0.1587
Step 3: Finally, convert the decimal to a percentage:
0.1587 * 100 = 15.87%
Approximately 15.87% of light bulbs have a life of more than 3000 hours.