AP Stats FRQ Practice Prompt Samples & Feedback (Unit 5)

The FRQ Practice Prompt

FRQ Writing Samples and Feedback

FRQ Practice Submission 1

In part (a), you appear to misunderstand what you’re being asked to describe. You describe the distribution provided by the histogram. However, the histogram is really providing the distribution of the “population” in this scenario; we are being asked to describe what it would look like if we took repeated samples of 40 eruptions from the graph shown and create a new graph of x-bars. Since 40 > 30, the shape of the original distribution (the one you described) doesn’t matter; the Central Limit Theorem applies and we can describe the resulting sampling distribution as approximately normal, with a mean of 210 seconds and a standard error of 68/sqrt(40) seconds [using formulas from our formula sheet].

The misconception in part (a) then extends to part (b) - you use the “original” standard deviation when we should instead use the standard error of 68/sqrt(40) = 10.751 seconds. This impacts the z-score you would get an ultimately your associated probability. In previous rubrics, you would still get partial credit for calculating the probability that you did, because you did all of your work correctly given the mistake you made.

Another small thing: you had the right idea checking the 10% condition, but used the wrong numbers. We should be comparing 40 to 421 (and since 40(10) = 400 < 421, the condition is still met). I am unsure whether that would be penalized on a typical rubric.

FRQ Practice Submission 2

In part (a), you correctly describe the shape, center, and spread of the sampling distribution, citing the Central Limit Theorem as the reason for the distribution being “approximately normal.” What you should be careful with is that you start by saying “the population is approximately normal”, when it’s the sampling distribution that is approximately normal. Unfortunately, that would sometimes be enough to lower your score by a level (from fully correct to partially correct); you’ve used the wrong statistical term.

In part (b), you do a good job of communicating the probability you are asked to find, then carry out calculations correctly and answer in context. Nice job!

FRQ Practice Submission 3

Good on both parts! In part (a), you give correct descriptions for shape, center, and spread, and correctly invoke the Central Limit Theorem since n = 40 > 30. In part (b), you calculate the correct probability. Small note on notation: P(X < 200) should be P(x-bar < 200). I know that we can’t format “x-bar” on here, but you were asked about a sample mean so we need to use the appropriate symbol. That actually could be enough to bump you down a scoring level, so watch your symbols/notation carefully.

FRQ Practice Submission 4

Well done! You’ve correctly invoked the CLT in part (a) to justify your shape being approximately normal, while giving correct measures of center and spread. Be careful - your first two words are “the sample” instead of “the sampling distribution” - there’s a big difference in those two things. There are no issues in part (b) - nice job!

FRQ Practice Submission 5

• A. The sampling distribution of sample mean eruption length for random samples of 40 eruptions would be approximately normal due to the Central Limit Theorem — because the sample size is greater than 30, the sampling distribution will be approximately normal.
• B. The probability that the sample mean eruption length for a random sample of 40 eruptions is 200 seconds or less is about 44.04%. The Z-score would be about -0.15.

For part (a), you correctly identify the shape as “approximately normal” due to the CLT (and give the correct reason, n = 40 > 30). However, a description of a distribution (of any type) should include measures of center and spread to go with shape. (Many teachers use “S.O.C.S.” or “C.U.S.S.” as acronyms to help students remember - Shape/Outliers/Center/Spread or Center/Unusual Features/Shape/Spread). In this case, you did not mention the mean of the sampling distribution (which would still be 210) or the standard error (which would be 68/sqrt(40) = 10.75). This then impacted your probability calculation in part (b). You correctly used z-scores and did a correct calculation for what your z-score was, but would only earn partial credit from not calculating the standard error in part (a)

FRQ Practice Submission 6

Perfect all around!

FRQ Practice Submission 7

part (a) has everything needed to describe a distribution (center, shape, and spread are mentioned, so no need for outliers/range), though you should show where the 10.75 seconds calculation came from. Part b, you’ve done all appropriate calculations.

FRQ Practice Submission 8

Solid work! The only possible issue: in part (a), you mention the shape as “approximately normal”, but don’t give the reason for that until part (b) (since n = 40 > 30, the CLT applies). On some rubrics, we’d be able to give you retroactive credit for part (a) based on that description in part (b), but it’s always safe to show that the CLT applies whenever you’re citing a sampling distribution of x-bar being approximately normal.

FRQ Practice Submission 9

Perfect! You mention center, shape, and spread in part (a) - correctly applying the CLT - and do appropriate calculations in part (b).

FRQ Practice Submission 10

Perfect! You’ve correctly justified with the CLT and then done appropriate calculations in part (b).

FRQ Practice Submission 11

Nice work. It’s a small thing, but it matters: when using the CLT we have to say approximately normal. t-distributions are never perfectly normal until we hit infinity as a sample size (which is of course impossible). It would result in partial credit on an otherwise perfect response.

FRQ Practice Submission 12

Correct on both parts. While you don’t say “Central Limit Theorem” in part (a), you justify the shape (approximately normal) based on the sample size, so that will count.