20000 light bulbs are tested to see how long they last. The collected data is normally distributed. If 95% of the light bulbs lasted within 29800 and 31100 hours, what is the standard deviation? The mean is 30,000.
This means that both 29800 and 31100 are 2 standard deviations away from the mean.
To find the standard deviation, simply subtract the mean (30000) from 31100, then divide it by 2 (because of the 2 SDs).
SD=31100-300002
SD=11002
SD=550
SD=550
Question 2 of 5
2. Question
20000 light bulbs are tested to see how long they last. The collected data is normally distributed. Within how many hours did 68% of the light bulbs last?
We are asked about how many light bulbs last less than 29450 hours.
First, we find the percentage of these light bulbs.
All the data below the mean (30000) is 50%.
Knowing that 68% of the data lies 1 SD below and above the mean, we can say that the data between 29450 and 30000 is 34% because it is 1 SD just below the mean.
Compute for the shaded region.
50%-34%=16%
The percentage of the data below 29450 is 16%.
Simply get 16% of all the light bulbs tested.
16100=0.16
20000×0.16=3200
Hence, 3200 of the light bulbs lasted less than 29450 hours.
3200
Question 4 of 5
4. Question
Skull widths of a group of adults are normally distributed with a standard deviation of 52 mm. What is the mean width if 2.5% of the skull widths are less than 1276 mm?
We know that 50% of the data lies on the first half of the curve.
Also, remember that 95% of the data lies 2 standard deviations above and below the mean. This leaves us with 5% for the rest of the curve, specifically, 2.5% for each tail outside the 95%.
Subtract 2.5% from 50% to find the percentage of the data between 1276 and the mean.
50%-2.5%=47.5%
47.5% is actually half of 95%. This means that there are 2 standard deviations between 1276 and the mean.
Given that the standard deviation is 52 mm, we can easily compute for the mean width.
1276+52+52=1380
The mean width is 1380 mm.
1380
Question 5 of 5
5. Question
Skull widths of a group of adults are normally distributed with a standard deviation of 52 mm. If there are 10000 adult skulls, how many skulls have widths between 1224 and 1484 mm?
