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Probability and Statistics Quiz #2 Name: 1) What is the total area under any arbitrary density curve? 1 2) Fill in the blanks: 68 % of the observations fall within one standard deviation of the mean. 95 % of the observations fall within two standard deviations of the mean. 99.7 % of the observations fall within three standard deviations of the mean. 3) If X N ( ; ) ; then what do you have to do to X to get it’s distribution standard normal? X 4) Given a normal density curve, what is a cumulative proportion at a …xed point z? The area to the left of z: 5) The distribution of ACT scores for more than 1 million students in a recent high school graduating class was roughly Normal with mean = 20 and standard deviation = 5: The SAT scores for 1.4 million students in the same graduating class were roughly Normal with mean = 1000 and standard deviation = 200: A) Tonya scores 1300 on the SAT. Jermaine scores 30 on the ACT. Assuming that both tests measure the same thing, who has the higher score? Report the z scores for both students. SAT(Tonya): 1300 1000 = 32 200 ACT(Jermaine): 30 20 = 2: 5 Therefore, Jermaine had the higher score. B) What score on on the SAT is equilvalent to Jermaine’s score from part A)? 1000 2 = x 200 ) x 1000 = 400 ) x = 1400: C) What percentile (i.e. cumulative proportion as a percent) is Tonya’s score from part A)? By table A; 3 = 93:31% P Z 2 D) What SAT scores make up the top 15.87% of all scores? P [Z > z] = :1587 ) P [Z < z] = 1 :1587 = 0:841 3 By table A this means that z = 1: 1000 = 1 ) X 1000 = 200 ) X = 1200: So, X 200