1. Let X = the number of times a person enrolls in Math 094 at South, where they cannot take a class more than three times. Use the probability distribution function to find the following: P(x) XP(x) 0.24 a. Find the probability a person does not take Math 094. 1 0.61 2 0.12 3 0.03 b. Find the probability a person takes Math 094 more than once. c. Find the probability a person takes Math 094 less than three times. d. Complete the table and find the expected (mean) number of times a person will take Math 094. 2. We perform the experiment of flipping a fair coin four times, and are interested in the number of times we will get heads ( out of the four tosses). a . Verify that this is a binomial distribution, (identify n, a success and p)- b. Complete the probability distribution table. c. Find the probability that we get exactly two heads. X P (X ) d. Find the probability we get at most two heads. e. Find the probability we get heads more than once. - 2. f. Find the probability we get all heads. 3 g. What is the mean of this distribution? h. What is the standard deviation?3. The Rocket Club plans to sell 100 raffle tickets, each for $5.00. The winner will receive half of the revenue generated by the raffle ($250). What is the expected value of buying a ticket? Should you buy one? 4. The number of minutes late a tardy student arrives to class is Uniformly Distributed between 0 and 12 minutes, a. Find the probability a tardy student is exactly five minutes late. b. Find the probability a tardy student is more than five minutes late. c. Find the probability a tardy student is between five and ten minutes late. d. What is the mean or expected number of minutes a tardy student will be late?4. Quiz scores are normally distributed with a mean of 72 and a standard deviation of 9. a. Find the z-score for a person who scored 95. b. What does a z-score of negative one represent? c. What is the probability a person scored more than 85? d. What is the probability a person scored less than 72? e. What is the probability a person scored exactly 95? f. What score separates the top 10% of the quiz scores?5. Men's heights are normally distributed with a mean of 70 inches and a standard deviation of 4 inches. Find the following probabilities, using proper Probability notation and indicating which function(s) were used in your calculator to get your results. a. Find the probability that an individual randomly chosen male is taller than 75 inches. b. Find the probability that individual randomly chosen man's height is between 60 and 66 inches. Suppose that a random sample of 16 men is selected. c. Find the probability that the sample mean height of the sixteen men is less than 72 inches. d. Find the probability that the sample mean height of the sixteen men is exactly 72 inches