PROBLEM: Mrs. Patenaude asked each student in her APO Statistics class to toss a coin and record the result. There were 28 students in the class. Assume that all the coins are fair. Let X = the number of coins that landed heads. Here is a histogram of the probability distribution of X: 016 - 014 0.12 - Probabilr 0.02 - 0.00 - 10 15 X . Number of hoads (a) What probability distribution does X have? Justify your answer. (b) Describe the shape of the probability distribution. ALTERNATE EXAMPLE (page 416) More binomial coin tossing Describing a binomial distribution PROBLEM: Mrs. Patenaude asked each of the 28 students in her AP Statistics class to toss a coin and record the result. Assume that all the coins are fair. Let X = the number of coins that landed heads. Here is a histogram of the probability distribution of X: (a) Calculate and interpret the mean of X. (b) Calculate and interpret the standard deviation of X. PROBLEM: The Australian Official Lottery has scratch-off instant lottery tickets that can be purchased for $1. The probability of winning a prize is 1 in 4. Mr. Urban decides that he will buy lottery tickets until he finds a winner, and then he will quit. Let X = the number of lottery tickets needed to get the first winner. (a) Find the probability Mr. Urban buys exactly 8 lottery tickets in order to get the first winner. (b) Find P(X 2 5) and interpret this value in context