Answer the following questions

Math 231 Name: 562021 Exam II (Due: 6/5, 11:59pm) Points: (1-2) Determine whether the random variable x is discrete or continuous, Explain, 1. Let x represent the number of pumps in use at a gas station. 2. Let x represent the weight of a truck at a weigh station. 3, Find the mean, variance, and standard deviation of the probability distribution. iP(X) (x - P) P(2) 15 0.134 0.780 01053 0.006 120 0.021 4. Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. 1 =120, p =0.4 5. Thirty-nine percent of U.S. adults have a gun in their home. You randomly select 12 U.S. adults. Find the probability that the number of U.S. adults who have a gun in their home is (a) exactly two (b) at least two (c) more than two13. Find the 2-score that has 30.5% of the distribution's area to its right. 14. Find the positive z-score for which 940% of the distribution's area lies between -z and z. 15. What is the longest braking distance of a sedan that can be in the bottom 20% of braking distances? (#16-19) The driving distance (In miles) to work of 30 people are shown in the table at the right. Assume the population standard deviation is 8 miles. 16. Find the point estimate of the population mean j. Driving disdances In work jin miles 6 13 2 12 17. The margin of error for a 95% confidence Interval. 10. Construct a 95%% confidence interval for the population mean. 19. Determine the minimum sample size required to be 996 confident that the sample mean driving distance to work is within 2 miles of the population mean driving distance to work.20. Use the confidence interval to find the margin of error and the sample mean. (20,75, 24.10) 21. Find the critical value to for the level of confidence c and sample size n. 1.68) (10-11) The random variable x is normally distributed with mean j = 74 and standard deviation a = 8. Find the indicated probability. 10. P(x