HW19 - 50 draws we get less than 1 purple ball? (5) What is...

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ECO220Y: Homework, Lecture 19 Readings: Sections 9.2 Exercises: 9.30, 9.32, 9.34, 9.36, 9.40, Applets (CD-ROM): Applet 13 (page 312) Problems: Consider the box shown below, which contains 30 balls. Consider sampling 50 balls with replacement from this box. (It means that each time you draw a ball, you return the ball you drew last time. In this way, the number of balls in the box is always 30 when you draw.) (1) Define X as number of 1’s (red balls) in 50 draws with replacement. Is the normal approximation to the sampling distribution of the proportion reasonable? (2) Given your answer to (1), what is the chance that in the 50 draws we get more than 20 red balls? (3) Is the sampling distribution of the proportion of purple balls (3’s) in 50 draws with replacement reasonably approximated as normal? (4) Given your answer to (3), what is the chance that in
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Unformatted text preview: 50 draws we get less than 1 purple ball? (5) What is the minimum number of draws with replacement required such that the sampling distribution of the sample proportion of purple balls is reasonably approximated as normal? (6) If you sample 50 balls with replacement, which sample proportions are approximately normally distributed? Fill in the table below. Sample proportion Expected value Standard error (se) Approx. normally distributed? Of maroon balls (1s) Of green balls (2s) Of purple balls (3s) Of pink balls (4s) Of yellow balls (5s) Of orange balls (7s) Of blue balls (9s) (7) [OPTIONAL] How can you think about the result that the Binomial distribution approaches a bell shape as the number of trials goes up as an application of the CLT? 5 5 5 5 5 9 9 9 9 1 1 1 1 1 1 1 1 7 7 7 2 2 2 2 2 2 4 4 3 5...
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