# a) Getting 10 +/- 2 head in 20 tosses is the same probability as getting +/- heads in 320 tosses

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1 Question 1 pertains to tossing a fair coin (8 pts.) Fill in the blanks with the correct numbers to make the 2 scenarios equally likely: a) Getting 10 +/- 2 head in 20 tosses is the same probability as getting +/- heads in 320 tosses b) Getting 50% +/- 10% heads in 10 tosses is the same probability as getting % +/- % heads in 1,000 tosses Question 2 pertains to the probability histograms below which display chances for coin tosses and dice rolls. (12 pts.) Match the histograms with their description by writing the correct letter in each blank. Use each histogram exactly once. i) The probability histogram for tossing a fair coin twice and counting the total number of heads is ii) iii) iv) The probability histogram for tossing a fair coin 3 times and counting the total number of heads is The probability histogram for tossing a fair coin 100 times and counting the total number of heads is The probability histogram for rolling a fair die once and counting the number of spots is v) The probability histogram for rolling a fair die twice and counting the total number of spots is vi) The probability histogram for rolling a fair die three times and counting the total number of spots is Histogram A Histogram B Histogram C Histogram D Histogram E Histogram F 1 of 5 pages (11 problems)

2 Question 3 (6 pts.) Look at the 3 boxes below. In each box there are tickets with numbers written on them. Box A Box B Box C a. Which box has the largest SD? Box (2 pts.) Which one has the smallest? Box (2 pts.) (Fill in each blank with the correct letter) b. (2 pts.) Suppose we add 5 to the number on each of the 9 tickets above. How would the SD in each box change? i. The SD would stay the same in all the boxes. ii. The SD would increase in all the boxes. iii. The SD would decrease in all the boxes. iv. The SD would increase or decrease depending on the box. Question 4 (6 pts.) Fill in the 6 blanks below with the correct numbers to make the statements true. a) (3 pts) The largest the SD of a 0-1 box can be is. This happens when the box has % 0s and % 1s. b) (3 pts) The smallest the SD of a 0-1 box can be is. This happens when the box has % 0s and % 1s. Question 5 pertains to the following situation: (18 pts.) 64 draws are made at random with replacement from the box containing 6 tickets: The SD of the box is 2. a) (2pts.) The smallest the sum of the 64 draws could possibly be is and the largest the sum could be is b) (2pts.) The expected value for the sum of the 64 draws is c) (2pts.) The SE of the sum of the 64 draws is d) (4pts.) Use the normal approximation and your answers from (b) and (c) above to find the chance that the sum of the 64 draws will be less than 132? i) First calculate the Z score. Show work. Circle answer. (2 pts.) ii) Now mark the Z score accurately and shade the area that represents the chance of getting less than 132 Round the middle area given in the table to the nearest whole number. (1 pt. for shading) Chance = % (1 pt.) e) (2pts.) What is the expected value for the average of the 64 draws? f) (2pts.) What is the SE of the average of the 64 draws? Show work Hint: For parts g and h, draw a new box. g) (2pts.) What is the expected value for the number of 2s drawn in 64 draws? Show work h) (2pts.) What is the SE of the number of 2s drawn in 64 draws? Show work 2 of 5 pages (11 problems)

3 Question 6 (4 pts.) ABC news conducted a public opinion poll where any Internet user could go and cast his or her vote. On Aug 12, 2016, the question was: Who are you voting for? 63,536 people voted, 70% voted Trump and 30% did not vote for Trump. a) (2 pts.) What most closely resembles the relevant box model? i) A box model is not appropriate for this poll because the sample was not randomly selected. ii) It has 63,536 tickets; 70% marked 1 and 30% marked 0 iii) It has millions of tickets marked with 1 s and 0 s. The exact percentages are unknown but are estimated from the sample. b) (2 pts.) The main problem with this sample is i) Bias in the wording of the question. ii) Sample Size iii) Selection Bias since the people selected themselves Question 7 pertains to the following situation: (12 pts.) In roulette, there are 38 numbers, 0,00,1,2,3, Consider betting \$1 on the four numbers 1, 2, 3, and 4. If the ball lands on any of the 4 numbers, you win \$8, but if the ball lands on any other number, you lose \$1. Imagine playing this bet 100 times. a) (2 pts.) Which of the following describes the corresponding box model? Circle one: i) A box that contains two tickets: 1 marked 8 and 1 marked -1. ii) A box that contains 38 tickets: one each of 1, 2, 3,..., 36, 0, and 00. iii) A box that contains 38 tickets: four marked 8 and thirty-four marked -1. iv) A box that contains 38 tickets: eighteen 1's, eighteen -1's, and two 0's v) A box that contains 38 tickets: eighteen are 1's and twenty are -1's b) (2 pts.) The draws are made replacement. (Fill in the first blank with the # of draws and the second blank with either with or without ) c) (2 pts.) The average of the box is closest to. Leave your answer in fraction form. Show work below. d) (2 pts.) The SD of the box is closest to. Round to 2 decimal places. Show work below. e) (4 pts.) Use the normal curve to estimate the chance that you d win more than \$47 in 100 plays. The EV= \$-5 and the SE= \$28. i) (2 pts.) First calculate the Z score. Show work. Circle answer. ii) (2 pts.) Now mark the Z score accurately and shade the area that represents the chance of winning more than \$47 Round the middle area given in the table to the nearest whole number. (1 pt.) Chance = % (1pt.) of 5 pages (11 problems)

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