A soft white 3-way bulb has an average life of 1200 hours with a standard deviation of 50
hours. Find the proportion of the life of one of these bulbs between 1150 and 1300 hours.
To find the proportion of the life of one of these bulbs between 1150 and 1300 hours, you can use the standard normal distribution.
Step 1: Convert the given average life and standard deviation to z-scores.
The z-score formula is: z = (x - μ) / σ
Where:
- x is the given value (in this case, either 1150 or 1300 hours)
- μ is the mean (average life of 1200 hours)
- σ is the standard deviation (50 hours)
For the lower bound (1150 hours):
z = (1150 - 1200) / 50 = -0.50
For the upper bound (1300 hours):
z = (1300 - 1200) / 50 = 2.00
Step 2: Use a standard normal distribution table or calculator to find the proportion between these z-scores.
Using a standard normal distribution table or calculator, we can find the proportion between -0.50 and 2.00. The table or calculator will give you the area under the curve between these two z-scores.
Note: Some tables/calculators provide the area to the left of the z-score, while others provide the area to the right. Since we want the proportion between the two z-scores, we need to subtract the area to the left of the lower bound from the area to the left of the upper bound.
Let's assume the table or calculator gives us:
Area to the left of -0.50: 0.3085
Area to the left of 2.00: 0.9772
Proportion between 1150 and 1300 hours:
Proportion = Area to the left of 2.00 - Area to the left of -0.50
Proportion = 0.9772 - 0.3085
Therefore, the proportion of the life of one of these bulbs between 1150 and 1300 hours is approximately 0.6687 or 66.87%.
you can play around with Z-table stuff here:
http://davidmlane.com/hyperstat/z_table.html