you can play around with Z-table stuff here:
http://davidmlane.com/hyperstat/z_table.html
hours. Find the proportion of the life of one of these bulbs between 1150 and 1300 hours.
http://davidmlane.com/hyperstat/z_table.html
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%.