This is a homework:
1) Suppose that a randomly selected patron waits for their drink at the campus coffee shop is uniformly distributed between zero and four minutes. What is the average waiting time and standard deviation of waiting time? Round your standard deviation calculation to three decimals.
2) Suppose that the random variable x has a uniform distribution with c = 2 and d = 8. a) Find P(3 <= x=""><=5). b)="" find="" p(1.5=""><= x=""><= 6.5).="" c)="" calculate="" the="" mean,="" variance,="" and="" standard="">
3) Assume x is a normally distributed random variable, what percentage of all possible observed values of x will be a) Within one standard deviation of the mean? b) Within two standard deviations of the mean? c) Within three standard deviations of the mean?
4) How does x relate to the mean m if the z value corresponding to x a) Equals zero. b) Is positive. c) Is negative.
5) Assume x is a normally distributed random variable with mean 30 and standard deviation 5. Find the z value for each of the following observed values of x: a) x=25 b) x=15 c) x=30 d) x=40 e) x=50 6) On Friday nights, the local pizza shop has demand that is normally distributed with a mean of 800 pizzas and a standard deviation of 75 pizzas. a) What is the probability that demand is 959 pizzas or less? b) What is the probability that demand is more than 1,004 pizzas? c) What is the probability that demand is less than 650 pizzas or greater than 950 pizzas? d) The store pre-makes the dough before the evening rush. How many pizza dough balls should they make in order to have only a 2.5 percent chance of running out of pizza dough? 7) The lifetimes of a particular brand of car stereo are normally distributed with a mean of eight years and a standard deviation of six months. Find each of the following probabilities where x denotes the lifetime in years. a) P(7 <= x=""><= 9)="" b)=""><><=9.5) c)="" p(6.5=""><=x><=7.5) d)="" p(x="">= 8) e) P(x <= 7)="" f)="" p(x="">=7) g) P(x <=10) h)="" p(x="">10) 8) A very large class has exams scores that are normally distributed. Two students receive raw scores of 63 and 93, which correspond to z scores of -1 and 1.5, respectively. Find the mean and standard deviation of the distribution of raw exam scores.
9) Suppose that annual health care expenses for an individual are normally distributed with a mean of $3,000 and a standard deviation of $500. The government has mandated a health insurance premium reduction if a policyholder’s health care expenses do not exceed a specified dollar amount. What dollar amount should be established if the government wants to ensure individuals having the lowest 33 percent health care expenses receive the premium reduction?