Empirical Rule Worksheet, Schemes and Mind Maps of Statistics

Download Empirical Rule Worksheet and more Schemes and Mind Maps Statistics in PDF only on Docsity! Abe Mirza Part 1 Practice Problems Statistics Empirical Rule 1. Given an approximately normal distribution with a mean of 159 and a standard deviation of 70. a) What percent of values are within the interval (89, 299)? _______________ b) What percent of values are within the interval (19, 159)? _______________ c) What interval contains 99.7% of all values? _______________ d) What percent of values are above 229? _______________ e) What percent of values are outside the interval (19, 229)? _______________ Question B There were six different stat classes that were offered last semester; one student was randomly selected from each class with his/her final score and the class average and standard deviation. Find the z-score for each student. Joe got score of 83 when the class average was 71 with standard deviation of 6.5. _____________ Moe got score of 88 when the class average was 76 with standard deviation of 7.5. _____________ Nielo got score of 77 when the class average was 72 with standard deviation of 2.3. _____________ April got score of 82 when the class average was 72 with standard deviation of 5.5. _____________ Max got score of 82 when the class average was 71 with standard deviation of 5. _____________ Alex got score of 82 when the class average was 72 with standard deviation of 6. _____________ Answer the following questions: a) Who did relatively better in the class than the rest? b) Who did relatively worse in the class than the rest? c) Who got scores that can be considered unusual? 7. 500 freshmen at Schaumburg High School took an algebra test. The scores were distributed normally with a mean of 75 and a standard deviation of 7. Label the mean and three standard deviations from the mean. Answer the following questions based on the data: a) What percentage of scores are between scores 61 and 82? b) What percentage of scores are between scores 75 and 82? c) What percentage of scores are between scores 61 and 89? d) What percentage of scores is less than a score of 61? e) What percentage of scores is greater than a score of 96? f) Approximately how many algebra students scored between 61 and 89? g) Approximately how many algebra students scored between 68 and 82? h) Approximately how many algebra students scored between 61 and 75? i) Approximately how many algebra students scored between 89 and 96? j) Approximately how many algebra students scored higher than 89? 10) The table below represents a random sample of the number of deaths per 100 cases for a certain illness over time. If a person infected with this illness is randomly selected from all infected people, find the probability that the person lives 3-4 years after diagnosis. Express your answer as a simplified fraction and as a decimal. Years after Diagnosis Number deaths 1-2 15 3-4 35 5-6 16 7-8 9 9-10 6 11-12 4 13-14 2 15+ 13 A) 1 35 ; 0.029 B) 35 100 ; 0.35 C) 35 65 ; 0.538 D) 7 120 ; 0.058 10) 11) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 2. A) 0 B) 1 6 C) 2 D) 1 3 11) 12) A fair coin is tossed two times in succession.  The set of equally likely outcomes is {HH, HT, TH, TT}. Find the probability of getting the same outcome on each toss. A) 3 4 B) 1 4 C) 1 D) 1 2 12) 13) A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4),  (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}. Find the probability of getting two numbers whose sum is greater than 10. A) 1 18 B) 3 C) 5 18 D) 1 12 13) 14) A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4),  (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}. Find the probability of getting two numbers whose sum is less than 13. A) 1 2 B) 1 4 C) 1 D) 0 14) 15) Three fair coins are tossed in the air and land on a table.  The up side of each coin is noted.  How many elements are there in the sample space? A) 4 B) 6 C) 8 D) 3 15) 16) In a survey of college students, 880 said that they have cheated on an exam and 1721  said that they have not. If one college student is selected at random, find the probability that the student has cheated on an exam. A) 880 2601 B) 2601 880 C) 1721 2601 D) 2601 1721 16) 28 8 Probability 1) If 25% of U.S. federal prison inmates are not U.S. citizens, find the probability that 2 randomly selected inmates will not be U.S. citizens. 2) If 2 cards are selected from a standard deck of cards. The first card is placed back in the deck before the second card is drawn. Find the following probabilities: a) P(Heart and club) d) P(2 Aces) b) P( Red card and 4 of spades) e) P(Queen of hearts and King) c) P(Spade and Ace of hearts) f) P(2 of the same card) 3) Find the same probabilities for problem #19 but this time, the card is not placed back in the deck before the 2nd card is drawn. d) P(Heart and club) d) P(2 Aces) e) P( Red card and 4 of spades) e) P(Queen of hearts and King) f) P(Spade and Ace of hearts) f) P(2 of the same card) Answers Questions B. Name x x s x xz s − = Joe 83 71 6.5 1.85 Moe 88 76 7.5 1.60 Nielo 77 72 2.3 2.17 April 82 72 5.5 1.82 Max 82 71 5 2.20 Alex 82 72 6 1.67 a)Max b) Moe c) Nielo and Max Answer Key Testname: UNTITLED1 1) B 2) A 3) B 4) B 5) A 6) D 7) B 8) A 9) B 10) B 11) B 12) D 13) D 14) C 15) C 16) A 29 9