1. The number of motor vehicle accidents per student in a recent year at college is given in this frequency distribution chart. ACCIDENTS STUDENTS 0 6701 4602 3803 2254 2055 40 a) Construct a Probability Distribution b) Find the mean and standard deviation.2. Give two examples each of discrete random variables, and continuous random variables. 3. Eighty-five percent of all small businesses in the U.S. have a Web site. If you randomly select 10 small businesses: a) What is the probability that exactly nine of them have a Web site?b) The probability that at least one of them have a Web site?c) The probability that all of them have a Web site?4. Several students are unprepared for a multiple-choice quiz with 25 questions, and all of their answers are guesses. Each question has 4 possible answers, but only one is correct.a) Does this procedure results in a Binomial Distribution? If yes, identify all requirements needed for this particular procedure.b) Find the mean and standard deviation.c) Use part b) to indicate whether is usual or unusual for a student to score by guessing at least 9 correct answers? Explain why or why not.5. Women’s weighs are normally distributed with mean and standard deviation Find the z-scores for the following values:a) b) 6. The Beanstalk Club, a social organization for tall people, has a requirement that women must be at least 70 inches tall. What percentage of women meets that requirement?(Heights of women are normally distributed with and )7. Attendance to a local sports event averages about 8000 people per week, with standard deviation of about 500. Assume that attendance figures follow a normal distribution. a) What is the probability that that attendance, any given week, will be fewer than 7200 people? b) What is the probability that attendance will be between 7700 and 8800 people?8. Scores for an entry exam to a university are normally distributed with a mean of 70 and a standard deviation of 4.5. a) If the top 10% are admitted with a full scholarship, what is the lowest score a student can obtain to earn a full scholarship? b) The university decides that students, who score below or at the 10th percentile, must take remedial courses. If a student scores 63 on the entry exam, will he/she be taking remedial courses? Explain why.9. Scores for the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 112. Randomly selected men are given the Columbia Review Course before taking the SAT test. Assume that the course has no effect.a) If 16 students are randomly selected, find the sample mean and the sample standard deviation.b) In a classroom with16 students , find the probability that their mean score is at least 590.10. When a murder occurs, it is known that 64% of the victims actually knew the person who committed the murder. Suppose that 63 current unsolved murders are randomly selected, what is the probability that at least 35 of the victims knew the murderer?( Is this a binomial distribution problem?)