3.23 For the following situations, identify whether or not X has a binomial distribution. If it does, give n and p; if not, explain why. (a) Every day Amy goes out for lunch there is a 25% chance she will choose pizza. Let X be the number of times she chose pizza last week. (b) Brenda plays basketball, and there is a 60% she makes a free throw. Let X be the number of successful baskets she makes in a game. (c) A bowl contains 100 red candies and 150 blue candies. Carl reaches and takes out a sample of 10 candies. Let X be the number of red candies in his sample. (d) Evan is reading a 600-page book. On even-numbered pages, there is a 1% chance of a typo. On odd-numbered pages, there is a 2% chance of a typo. Let X be the number of typos in the book. (e) Fran is reading a 600-page book. The number of typos on each page has a Bernoulli distribution with p = 0.01. Let X be the number of typos in the book. 3.25 A bag of 16 balls contains one red, three yellow, five green, and seven blue balls. Suppose four balls are picked, sampling with replacement. (a) Find the probability that the sample contains at least two green balls. (b) Find the probability that each of the balls in the sample is a different color. (c) Repeat these two problems for the case when the sampling is without replacement 3.31 The number of eggs a chicken hatches is a Poisson random variable. The probability that the chicken hatches no eggs is 0.10. What is the probability that she hatches at least two eggs? 3.32 Hemocytometer slides are used to count cells and other microscopic particles. They consist of glass engraved with a laser-etched grid. The size of the grid is known making it possible to count the number of particles in a specific volume of fluid. (a) A hemocytometer slide used to count red blood cells has 160 squares. The average number of blood cells per square is 4.375. What is the probability that one square contains between 3 and 6 cells? (b) Modify the Balls.R script to simulate the distribution of 700 red blood cells on a hemocytometer slide. Use your simulation to estimate the probability that a square contains between 3 and 6 cells. 3.33 Cars pass a busy intersection at a rate of approximately 16 cars per minute. What is the probability that at least 1000 cars will cross the intersection in the next hour? (Hint: What is the rate per hour?)