Stat 100

[BarTopDancer]

Thank you!!!!

[BarTopDancer]

OK, here are my answers:

your grade point average – an outlier towards the high end. Since GPA at PSU can only be 4.0, and GPA in college is usually a B or C average, I would want to my GPA to be an outlier at the high end of the GPA scale, separating myself from the mean.

b. age at which you graduate from college – this depends on when you start college, and where you attend college. Depending on when you start, how many classes you take and if you pass them on the first attempt can greatly vary the age you are when you graduate from college In CA it takes about 6 years to complete a Bachelor’s degree. Since I am 31, I am most likely already an outlier. This could be answered either way: an outlier towards the younger age, the mean, or an outlier towards an older age since I am graduating college. Since I am already an outlier, and I am ecstatic to graduate in the fall, I have to say that I prefer my value to be an outlier when I graduate.

c. monthly rent for your first apartment mean for the quality of apartment being rented. If the apartment is to cheap, it may be in an extremely unsafe area, or have underlying issues that aren’t visible upon viewing or move-in.

[BarTopDancer]

One more (for now). I may have one later but I know you guys are getting ready, if not already are camping.

8. Suppose a STAT 100 exam has 50 questions each worth 2 points. The results for this exam follow a normal distribution where the mean is 80 points with a standard deviation of 6 points.

Part A: Approximately 95% of the exam scores will be between what two values?

a. (80± 6) = (74 to 86) points
b. (80 ± 2  6) = (80 ± 12) = (68 to 92) points
c. (80 ± 3  6) = (80 ± 18) = (62 to 98) points
d. (80 ± 2) = (78 to 82) points

Approximately 95% of the exam scores will be between 62 to 98 points.

Part B: Would you expect a student to score as low as 50 points on this exam? Provide reasoning.
I would not expect a student to score as low as 50 points on this exam. I would hope students studied and absorbed knowledge to perform better. However, some students scored 62 points, and there are 5% of the students left. Based on the mean, a student could score as low as 50 points.

[Moonliner]

As stated there is nothing in the question that implies you get to choose to be either a high or low outlier. Your choice is only outlier or mean.

So using the GPA example, if you choose outlier you are taking a chance at falling on the low side: A failing grade. Whereas if you choose the mean you are guaranteed to pass but not to excel.


(Note: I am assuming that in the original statement of the problem, the part after the '-' is your initial answer and not part of the supplied question)

[BarTopDancer]

Thanks Moonie. Now I am back to being confused and overthinking. Maybe I'll add that too.

Ok,

your grade point average – The mean. an outlier could mean I’m towards the high end or the low end of the GPA scale. Since GPA at PSU can only be 4.0, and GPA in college is usually a B or C average, I would want to my GPA to be an outlier at the high end of the GPA scale, separating myself from the mean. But since I cannot pick to be at the high end of an outliner, I’d prefer my data value in this to be a mean when compared to others data values.

[Alex]

Your answers to #8 are incorrect.

Since this is homework, I am loathe to just tell you the correct answer on a factual question. But you didn't explain why you gave the answer you did for part 1.

So if you explain, I can perhaps point you into the right direction (and being shown where you went wrong will be more helpful than just being told the right answer).


For part 2, the key thing to note about your answer is that ultimately you explained that it is possible for someone to score 50 points. That is irrefutably true (it is possible for someone to have had every even numbered score between zero and 100). But that wasn't the question, the question asks whether you expect someone to score that low.

So, since you've been told that the results followed a normal distribution, the first question you need to ask yourself is this: How many standard deviations is 50 from 80?

Then using what you know about how standard deviation correlates to percentage of results, reconsider the question asked.

[BarTopDancer]

Thanks Alex.

I don't want the answers to be handed to me(thank you). I want to understand so I can get the answers on my own (important for the tests).

I used a formula in the book following the Empirical Rule for the third standard deviation. I obviously didn't understand it correctly.

My original thought was A (between 74 and 86) because it has only 1 standard deviation. But the 2 points per question threw me off.

For part 2, I over thought the question. That is one of my challenges - over thinking these things.

Ultimately I would not expect a student to score 50 points on the exam. Even with the standard deviation of 6 points, the mean is high enough to expect students will score above 50 points.

[Alex]

A is also incorrect for Part 1. But now I'm scared I'm misremembering the % values for standard deviations (but I just confirmed I'm not). What percentage of results in a normal distribution are covered by the following:

1 standard deviation
2 standard deviations
3 standard deviations


The fact that each question on the test is worth 2 points is irrelevant to the answers. All you need is the mean score and the standard deviation. You don't need to know how many points each question was worth or how many points were possible.

The answers would be the same if each question were worth one point and there were 16,000 questions on the test.


For part 2, the key point of the question is that a score of 50 points is five standard deviations (30 point difference = 6*5) away from the mean. What percentage of results will be five or more standard deviations from the mean in a normal distribution?

[BarTopDancer]

OK, I think I understand part 1.

(80 ± 2 * 6) = (80 ± 12) = (68 to 92) points

The mean is 80. The standard deviation is 6. You have to take the Mean ± 2(SD). So 80 ± 2*6 = the answer.

Part 2.

I have no idea. I am so lost again. I don't even trust that my answer for A is correct anymore.

I think that 3 standard deviations is 18. But you already said C was incorrect for #1.

I'll look at it again in the morning. I appreciate your help.

[Alex]

Originally Posted by BarTopDancer

The mean is 80. The standard deviation is 6. You have to take the Mean ± 2(SD). So 80 ± 2*6 = the answer.

This is correct.

The empirical rule is 68-95-99.7, right? That means that for a normal distribution, one standard deviation will include about 68% of the population. Go out to 2 standard deviations and it will include about 95% of the population. 3 standard deviations takes you up to 99.7% of the population.

So, since the question asks about covering 95% of the results, that would be two standard deviations. That's the reasoning underlying the correct formula you gave. So Answer B (68 to 92) is correct.

Part 2.

I have no idea. I am so lost again.

You're correct that 3 standard deviations is ±18 points from the mean (62 to 98). And 5 standard deviations would be ±30 points.

Per the empirical rule, 99.7% of all results will be within just 3 standard deviations of the mean. So we know that only 0.3% of all results will be lower than 62 points or higher than 98 points.

I don't know if it is covered by your textbook but if you extend the empirical rule you get:

1 standard deviation = 68%
2 standard deviation = 97%
3 standard deviation = 99.7%
4 standard deviation = 99.99%
5 standard deviation = 99.9999% of all results

So, since a score of 50 is 5 standard deviations away from the mean, you would expect only 0.0001% of scores to be that far from the mean. Another way of saying that is you'd expect one student out of a million to score that low. Since it is extremely unlikely that a million students are taking the Stats 100 class you would not expect that anybody will score that low (though it remains statistically possible it is statistically improbable).