Question 1204995: In a factory that produces wire, the spooling machine is programmed to 3,500 feet of wire on each spool. The company ran the machine and then measured how much wire was actually on each spool. They found that the mean length was actually 3,510 feet and the standard deviation was 25 feet. They then ran the machine again and produced a sample of 400 spools of wire. Assume that the data is normally distributed.
1. Draw a normal distribution curve; be sure to include all the intervals and percentages.
2. What is the median and mode?
3. How many spools have at least 3,510 feet of wire?
4. How many spools have less than 3,485 feet of wire?
5. How many spools have between 3,485 and 3,560 feet of wire?
6. How many spools have between 3,460 and 3,535 feet of wire?
7. How many spools are within one standard deviation?
8. How many spools have less than 3,560 feet of wire?
9. How many spools make this inequality true: the amount of wire > 3,485 feet?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the mean of the population is 3510 and the population standard deviation is 25.
you run 400 spools through the machine.
1. Draw a normal distribution curve; be sure to include all the intervals and percentages.
each particular situation is drawn below.
2. What is the median and mode?
if it is a normal distribution, then the mean and the mode and the median are the same value at an average of 3510 per spool.
3. How many spools have at least 3,510 feet of wire?
to find the number, the proportions are multiplied by 400 to get an estimate of the approximate number of spools that satisfy the criteria.
since the mean is 3510, than half should have a mean less than 3510 and half should have a mean greater than 3510.
.5 * 400 = 200.
4. How many spools have less than 3,485 feet of wire?
.1587 * 400 = 63.48 = 63 rounded to the nearest integer.
5. How many spools have between 3,485 and 3,560 feet of wire?
.8186 * 400 = 327.44 = 327 rounded to the nearest integer.
6. How many spools have between 3,460 and 3,535 feet of wire?
.8186 * 400 = 327.44 = 327 rounded to the nearest integer.
7. How many spools are within one standard deviation?
1 standard deviation is 25.
to be within 1 standard deviation, then 3510 - 25 = 3485 on the low end, and 3510 + 25 = 3535 on the high end.
.6827 * 400 = 273.08 = 273 rounded to the nearest integer.
8. How many spools have less than 3,560 feet of wire?
.9772 * 400 = 390.88 = 391 rounded to the nearest integer.
9. How many spools make this inequality true: the amount of wire > 3,485 feet?
.8413 * 400 = 336.52 = 337 rounded to the nearest integer.
calculator used is at https://davidmlane.com/hyperstat/z_table.html
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