# Can you solve these math problems? (introductory college level)

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My daughter has a final coming up tomorrow and their are a few problems she doesn't understand on her practice test. If anyone would mind taking the time to thoroughly solve and explain these, she would be very grateful!!!

1. (Using the graph) What is the greatest range of speed for a roller coaster in this data set?

2. An internet site compares the strokes per round of two professional golfers: Jeff with a mean of 71.5 strokes and standard deviation of 2.3 strokes vs. Matt who has a mean of 70.1 strokes and standard deviation of 1.2 strokes. What is the coefficient of variation for each golfer? PUt Jeff's CV on the top line and Matt's CV on the bottom line. (Round to one decimal place)

3. Using the previous question, which golfer has more variation in golf strokes

4. Which is NOT true about Normal Distribution?

a. bell-shaped

b. symmetric with respect to standard diviation

c. total area under the curve = 1

d. 50% of data is below the mean

5. SHORT Answer: Assume that a normal distribution of data has a mean of 13 and standard deviation of 2. Use the 68-95-99.7 rule to find the percentage of values that lie below 17.

6. SHORT Answer: Assume that math test scores are normally distributed with a mean of 300 and standard deviation of 60. If you scored 240 on this practice exam, what percentage of those taking the test scored below you?

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1. (Using the graph) What is the greatest range of speed for a roller coaster in this data set?

This problem is written rather confusingly. The range of a data set is the difference between the maximum and minimum score. It looks from the graph like the speed of wooden roller coasters ranges from 20-80, and the speed of metal roller coasters rangers from 20-120. (But there's no unit given! 120 what?!) So I would say that the metal roller coasters tested have a range of 100 whatever-the-unit-is, and that's the greater range.

2. An internet site compares the strokes per round of two professional golfers: Jeff with a mean of 71.5 strokes and standard deviation of 2.3 strokes vs. Matt who has a mean of 70.1 strokes and standard deviation of 1.2 strokes. What is the coefficient of variation for each golfer? PUt Jeff's CV on the top line and Matt's CV on the bottom line. (Round to one decimal place)

We didn't use coefficient of variation, but there are instructions for how to figure it out here: http://www.westgard.com/lesson34.htm#6

3. Using the previous question, which golfer has more variation in golf strokes

Jeff's golf strokes show a larger standard deviation, which means that there's more variability. Standard deviation is a measure of how closely the items in a data set are grouped around the mean. The larger the SD, the more loosely the scores are grouped around the mean - and thus, the greater the variability.

4. Which is NOT true about Normal Distribution?

a. bell-shaped

b. symmetric with respect to standard diviation

c. total area under the curve = 1

d. 50% of data is below the mean

A normal distribution is an idealized bell-shaped curve. Because it's idealized, exactly half the scores fall above the mean and half fall below, so 50% of the data fall below the mean. The standard deviation for scores above the mean is equal to the standard deviation for scores below the mean (because it's a perfect bell shape), so (b) is also true. The total area under the curve is going to depend on the value of the mean and SD, so the correct answer is C.

Please tell me that the professor didn't spell it "diviation" or my heart will break.

5. SHORT Answer: Assume that a normal distribution of data has a mean of 13 and standard deviation of 2. Use the 68-95-99.7 rule to find the percentage of values that lie below 17.

Okay: draw a bell curve. Whenever you get a problem like this, you should start by drawing the curve. The highest point of the bell corresponds to the mean, which is 13. Mark off +1, +2, and +3 standard deviations going up from the mean - each one will be two points higher. You will find that a score of 17 is equal to +2 SD above the mean. (You can also mark off -1, -2, and -3 standard deviations going down from the mean, each one two points lower.)

In a normal distribution, 68% of scores will fall within 1 SD of the mean - in other words, between -1 SD and +1 SD, or for ths data set, between 11 and 15. 95% of scores will fall between -2 SD and +2 SD of the mean: for this sample, that means between 9 and 17. That leaves 5% of the scores to fall EITHER above 17 or below 9. Because the data is normally distributed, half of that 5% will be on the low end and half will be on the high end. You want to know what % of the values falls *below* 17, so take the 95% that fall between -2 and +2 SD and add the 2.5% that fall below -2 SD. 97.5% fall below 17.

6. SHORT Answer: Assume that math test scores are normally distributed with a mean of 300 and standard deviation of 60. If you scored 240 on this practice exam, what percentage of those taking the test scored below you?

Draw a bell curve. The mean is 300, right? Mark that at the top of the bell curve. The SD is 60, so your score of 60 is one SD below the mean. Draw that in. We know that in a normal curve, 50% of scores fall below the mean. We also know from the rule stated above that 68% of scores will fall within one SD of the mean. Half of those (34% is half of 68%) will be in between the mean and one SD above, and half (34%) will be between the mean and one SD below. If you scored at the mean, 50% of students would score below you. If you score one SD below the mean, (50 - 34) percent of students would score below you, which is 16%.

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4. Which is NOT true about Normal Distribution?

a. bell-shaped

b. symmetric with respect to standard diviation

c. total area under the curve = 1

d. 50% of data is below the mean

A normal distribution is an idealized bell-shaped curve. Because it's idealized, exactly half the scores fall above the mean and half fall below, so 50% of the data fall below the mean. The standard deviation for scores above the mean is equal to the standard deviation for scores below the mean (because it's a perfect bell shape), so ( B) is also true. The total area under the curve is going to depend on the value of the mean and SD, so the correct answer is C.

I like all of Rivka's responses except this one.  The correct answer is B.  The normal distribution is symmetric with respect to the mean, not with respect to standard deviation.  ("With respect to the mean" means that the mean is what acts like a mirror for the symmetry.  Rivka is correct that the std dev is going to be the same above and below the mean, but the mean itself is what the distribution is symmetric with respect to.)

The area under the curve from any x value to any other x value is the probability that a randomly selected data point will fall within that range.  The total area under the curve, then, will always equal 1, because if you include all possible x values, then your probability is 1.

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You're totally right. In my defense, I'm recovering from surgery and I still have anesthesia brain.

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You're totally right. In my defense, I'm recovering from surgery and I still have anesthesia brain.

LOL - you're excused. :lol:  I have new mommy brain, so I will confess that I waited until someone else had worked through all the problems and then just looked over your answers to see if there was anything I could add that might be helpful!

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Thanks so much! I will pass this info to my daughter and let her make heads or tails of it. lol And, no, I typed that word incorrectly. I actually realized I did when I was rereading it, but I didn't feel like fixing it. lol

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This one thread alone makes me terrified of homeschooling my rising 9th grader.

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This one thread alone makes me terrified of homeschooling my rising 9th grader.

Good grief, I thought the same thing. And our local CC is very homeschooler-unfriendly these days!

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This one thread alone makes me terrified of homeschooling my rising 9th grader.

These are stats problems -- unless you've had stats or a math for liberal arts course that included a significant amount of stats you shouldn't expect to understand them.

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I would not have been able to do half the things I can now without my son's interests being quite different than my own.  I am required to learn along with him and expect the same thing in high school.  The problems only occur if you hand over the book and back out of the way.  I was a STEM major, those problems were not an issue.  If you had asked me to translate Greek, it would have been completely undo-able.

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Have no fear, my daughter is a freshman in college. This is not part of her homeschooling course work.

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brought back memories. Both of my stats lecturers had strong other country accents. One I could understand the other only about 40%. Luckily I had a friend who was the other way round. Between us we managed notes.

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These are stats problems -- unless you've had stats or a math for liberal arts course that included a significant amount of stats you shouldn't expect to understand them.

This one thread alone makes me terrified of homeschooling my rising 9th grader.

Lots of people don't take stats in high school.  You're quite safe.   :001_smile:

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