2-dc_amp_nd_practice_test_key

Density Curves & The Normal Distribution Test MULTIPLE CHOICE ). /0253. M&L 1. The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches and standard deviation 2.5 inches. Only about 5% of young men have heights outside the range _,_/ ?é = ){Z—;@’ Xb‘ ~ 63 A4 (a) 65.5 inches to 70.5 inches @ 63 inches to 73 inches’ (c) 60.5 inches to 75.5 inches (d) 58 inches to 78 inches (e) None of the above. 2. The amount of time required for each of 100 mice to navigate through a maze was recorded. The histogram below shows the distribution of times, in seconds, for the 100 mice. ; L ; 60 70 80 90 10 110 120 Time {seconds) Which of the following values is closest to the standard deviation of the 100 times? (a) 2.5 seconds 10 seconds (c) 20 seconds (d) 50 seconds (e) 90 seconds 3. Zucchini weights are approximately normally distributed with mean 0.8 pound and standard deviation 0.25 pound. Which of the following shaded regions best represents the probability that arandomly selected zucchini will weigh between 0.55 pound and 1.3 pounds? \ (c) w2 wra (@) B () w053 e (e) pridse pilde

Density Curves & The Normal Distribution Test 4. The weight of adult male grizzly bears living in the wild in the continental United States is approximately normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is approximately normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds. Approximately, what would be the g weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear with a weight of 530 pounds? 70 — 570 2007 = 06 (a) 276 pounds @324 pounds (c) 330 pounds 50 00 (d) 340 pounds (e) 530 pounds 0 (p - )(1/ 7 5. A distribution of test scores is not symmetric. Which of the following is the best estimate of the zscore of the third quartile? E (a) 0.67 (b) 0.75 (c)1.00 (d) 1.41 @This z-score cannot be estimated from the given information. 6. For the density curve illustrated, which of the following is true? 0 1 2 |. The mean is smaller than the median. O Il. The proportion of outcomes between 0.1 and 0.7 is equal to 0.6. The proportion of outcomes exceeding 0.5 is equal to 0.75. (a) I only (b) Il only @III only (d) land Il (e) lland Il 7. Scores on the American College Test (ACT) are normally distributed with a mean of 18 and a standard deviation of 6. The interquartile range of the scores is approximately: Py A —0.675 = L~ (@s.1 (b) 12 ©6 d10.3 @7 : & X, 2 /8,953 a2.05 8. The test grades at a large school have an approximately normal distribution with a mean of 50. )/%”’ 8 077 % 58.09 What is the standard deviation of the data so that 80% of the students are within 12 points (above or below) the mean? /g (a) 5.875 9.375 (c) 10.375 (d) 14.5 (e) cannot be determined from the given information 3 X, Yy —~/ 982 = S g 369

Density Curves & The Normal Distribution Test 12. Mr. League was worried that the test you are currently taking (right now) would either be too easy or too difficult, so he wanted to do a “practice run” by giving it to his collection of pet spider monkeys (he has 24 of them — don't ask). The scores achieved by the monkeys took on a normal distribution with a mean score of 72 and a standard deviation of 7. Find the following, including sketches and calculations: ,,2/; (@) P(x>80) L]’(b) P(x<65) ,,Q/(c) P(70<x<80) PR = S | | so-7k Pz =1143) Zon7 Plec-l)zolsy 7 //,fl 26+ = £/ 17) 0. 456 13. Mr. League’s smartest pet spider monkey, Pretty Pete, scored in the 90" percentile when compared to his colleagues. What score did Pretty Pete achieve? (Show sketches and calculations) / a?ffl. = }fi;_/zz/ X » 7 - o2 50 77/ (8 w acap 14. Mr. League’s favorite, but dumbest, pet spider monkey, Colonel Fitzwilliam, forgot to turn his test in. When Mr. League found it on the floor, he had to re-calculate the summary statistics for his spider monkeys (it was still approximately a normal distribution for both parts aand 5 below). = /143 (a) If Colonel Fitzwilliam’s test score didn't change the distribution’s mean and decreased the standard deviation, what was Colonel Fitzwilliam's test score? 2/ CF's Test Score: 7j/ (b) If the Colonel’s score was a 62 and it increased the standard deviation to 7.2, and he scored in the 137 percentile, what was the new mean for all the tests? G A )y e ——— 7 A= ‘Q/ M = 70 /(0

Density Curves & The Normal Distribution Test 15. Mr. League is considering implementing one of two academic requirements (concerning test averages) for registering for the AP exam for his course. Over his entire career, student test averages are approximately normally distributed with a specified mean and standard deviation. s Academic Requirement Plan | calls for not allowing AP Statistics students to register for the exam if their test average falls more than 2 standard deviations below the specified mean. e Academic Requirement Plan il calls for not allowing AP Statistics students to register for the exam if their test average falls more than 1.5 interquartile ranges below the lower quartile of the specified population. (a) What proportion of students will not be able to take the exam under Academic Requirement Plan [? , fles-r) 200228 220 % of it vill nit Lo A+ pb S thar (b) What proportion of students will not be able to take the exam under Academic Requirement Plan 11? f6fe e Fermactl = —> 04T —(~0.676) .35 o — () 35) = ~ L7