"my,gpuziu-ifqmnm "fliys'ml'TKquk'lb. {heman} 53311me Apprmrimation II. A: may of 3300 people asked them whether they liked apple pie. Summa am @m afl independently with a 99.98% chance of liking apple pie. " (a) Why is the normal approximation not appr0priate in this instance? (b) Calculate the probability that all 3300 people will say they like apple pie. (0) Use a Poisson approximation to find the probability that 3297 of the people will say fia! they like apple pie. 2. A jar contains half green marbles and half red marbles. We draw out three marbles withmrt replacement. (a) Calculate the probability that all three marbles are red if we started out with 6 of each color in the jar. (b) Calculate the probability that all three marbles are red if we started out with 60 of each color in the jar. (0) Calculate the probability that all three marbles are red if we started out with 600 of each color in the jar. ' (d) Which of these is most like a Binomial Experiment? Lesson 8 Random Variables 3. I roll a fair six-sided die and let the random variable X be the number that comes up on the die. Calculate ' (a) P(3) (b) IP'{X 5 4} . (c) IP{(X - 3)2 S 3} 4. Suppose that X is a random variable with probability function(0) Calculate the probability that all three marbles are red if we MW m color in the jar. (cl) Which of these is most like a Binomial Experiment? Lesson 8 Random Variables 3. I roll a fair six-sided die and let the random variable X be the number that cam wa" iii?" Calculate (a) P(3) (b) IP{X s 4} (cr) P{(X "- 3)? s 3} 4. Suppose that X is a random variable With probability function and that the random variable Y 2 9X2 - 36X + 4. (a) What is the range of Y? (b) Calculate lP'{Y = 4}. (0) Calculate lP{Y = O}. '