What is the ev and the se of the number of times hed

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Unformatted text preview: f the ball lands on 1, € 2 or 3 the gambler wins $11, if the ball lands on any of the other 35 numbers the gambler loses $1. The roulette wheel € 38 slots numbered 1 ­36, 0 and 00. has a) Which is the appropriate box model? Circle one: i) The box has 38 tickets: 1 marked "1", 1 marked “2”, 1 marked “3”and 35 marked " ­1" ii) The box has 38 tickets: one each of 1, 2, 3, ..., 36, 0, and 00. iii) The box has 38 tickets: 3 marked "11" and 35 marked " ­1" iv) The box has 38 tickets: 3 marked "11" and 36 marked "0" b) How many draws from the box? _____100______ c) What is the average of the box? Write your answer as a fraction. (3(11) + 35( ­1))/38 = (33 ­35)/38 =  ­2/38 d) What is the SD of the box? Show work. Circle answer. Round your answer to 2 decimal places. − SD = 11− 1 3 35 ≅ 12 x 0.27 = 3.24 × 38 38 e) What is the Expected Value of the gambler’s winnings? (Show work.) € f) € EV€ = 100 ( ­2/38) = $  ­ 5.26 sum What is the SE of the gambler’s winnings? (Show work.) SEsum= 100 (3.24) = $ 32.40 € Page 3 Study Guide KEY for Exam 3 e) Now suppose you’re only interested in counting how many times the gambler would be expected to win if he played 100 times? What is the EV and the SE of the number of times he’d win if he played 100 times? (Hint: draw a new box with only 1’s and 0’s) i. EV of the number of 1 ’ s in 100 draws =______7.89_____ (2 pts.) New box has 3 1 ’ s and 35 0 ’ s so the average= 3/38 and the EVsum = 100 (3/38) = 7.89 ii. SE of the number of 1 ’ s in 100 draws =____2.7_________ (2 pts.) (Show work by computing the SD of the new box, then use it to calculate the SE for the sum of the 100 draws.) SD of box = € 3 35 = 0.27 so SEsum= 100 x 0.27= 2.7 × 38 38 € Page 4 Study Guide KEY for Exam 3 Chapter 14—The EV and SE of the Average and Percent • • • • EV of the average of n draws is just the average of the box. EV of the percent of 1’s in n draws from a 0 1 box is just the percent of 1’s in the box. SE of the average of n draws = SD of the box/ n SE of the percent of 1’s in n draws = SD of the box/ n (x 100%) Law of Averages: Compare SE of the sum to SE of the average and percent. € The SE for sums GROWS (is multiplied by n ) with more draws, the SE for averages € and percents SHRINKS (is divided by n ) with more draws. Practice Problems • 1) 100 draws are made at random with r€ eplacement from the box containing 5 tickets: 0...
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