STA218 Assignment for Quiz 5

Quiz on Thursday Feb 15th at the beginning of class

For this quiz, you will be allowed a single 8.5 by 11 one-sided formula sheet and a calculator. So write your formula sheet and use it to do the homework.

1. In Chapter 5, please read pages 158-168. You are responsible for the following concepts: Continuous random variable, Probability density function ("distribution") the normal probability distribution (but not the formula on page 160, standard normal random variable, how to look up standard normal; probabilities in the normal table (Table 3 in Appendix II), how to get probabilities for a general normal random variable with mean µ and standard deviation σ.

   Do exercises 5.2, 5.14, 5.16, 5.20, 5.22 (note that "retail" is collectors' retail, not the face value of the stamp), 5.24. (For 5.24b, there are infinitely many correct answers as the problem is stated. Your answer should be the limits of the shortest possible interval.), 5.62.

   Skip the rest of the chapter.

2. In Chapter 6, please read pages 188-203. You are responsible for the following concepts, some of which were introduced earlier in lecture: Simple random sample (you are not responsible for the formula telling you how to count the number of samples), Statisitc, Sampling distribution, Standard error of a statistic (general), Standard error of the mean (particular), Central limit theorem.

   Don't worry about the "restatement" of the Central limit theorem to apply to the sum of sample measurements (page 195). If you are asked a question about a sum, you can convert it into an equivalent question about the mean and use the ordinary Central limit theorem. For example, suppose that the number of new customers visiting a shop on succesive days are independent random variables with mean µ=6 and standard deviation σ=2. What is the probability that more than 390 new customers will visit the shop during the next 60 days? P(Sum > 390) = P(Sum/n > 390/60) = P(X-bar > 6.5). Any question about a sum or total can be transformed into a question about a mean using this approach.

   Also, skip the finite population correction factor given in the footnote on page 195. We'll cover it later.

   You are responsible for the properties of the sampling distribution of the mean given in the blue boox on page 199, iincluding the n=25 rule, which is really just a rough guideline.

   Do exercises 6.1, 6.2, 6.10, 6.15, 6.16, 6.17

3. In the game of roulette, there is a wheel with slots numbered 1-36, and another two slots labelled 0 and 00. You place a bet on a number. The casino employee spins the wheel, and if the ball falls in the slot you selected, you win. All the slots are equally likely, and as usual, the results of successive plays are independent. Suppose you get $25 if you win. You bet on the number "9" two hundred times in a row, wagering $1 each time. What is the probability that after your 200 plays, you will be behind?

   This is a hard problem, but you can do it by answering the following questions in order.

   1. Let X be your profit from playing the game once. What is the probability distribution of X?
   2. What is the expected value of X? (That's µ.) My answer is -13/38.
   3. What's σ? My answer is 4.001817
   4. This question about the sum is the same as asking the probability that the sample mean is less than what? My answer is 0/200 = zero.
   5. What's Z? My answer is +1.208976 ≈ 1.21
   6. Final answer? 0.8869

Do the assigned problems in preparation for the quiz. They are not to be handed in.