In the general hospital of Ottawa, a patient recovers from a surgery with the probability 0.50. What is the probability that at most 5 of the next 6 patients survive after surgery? None of them 0.882 0.738 0.982 0.469 Let X ~ Bin(50, 0.4) be a binomial random variable and Y ~ Geo(0.4) be a geometric random variable. Assume that X and Y are independent. What is ? 36.6 69.6 None of them 3.75 17.4 53.4 24.6 Var(X + 2Y) Let X be the cholesterol level for teenagers with age between 13 and 16. Suppose that X has a normal distribution with mean 160 mg/dl and standard deviation 32 mg/dl. We select a random sample of 16 teenagers with age between 13 and 16. What is the probability that the average cholesterol level for this sample is between 156 mg/dl and 164 mg/dl? None of them 0.5859 0.5328 0.4649 0.6247 0.3830 The length of time in minutes between consecutive calls to 911 in a small city has density e-x/2 f(x) = , 0 < x < , otherwise. What is the probability that the time between consecutive calls is greater than 20 minutes? None of them e-2 e-1 e4 e -10 The manufacturing of polymers for use in medicine is a prolific field of the chemical industry. We suppose that the quantity "X" of polymer (measured in mg) in a certain formulation is normally distributed. A sample of 10 measurements from X is given below: 603 534 542 591 680 489 516 570 592 654 We want to test Ho=530 versus H > 530 : at the significance level a = 0.02 . What is the decision and the value of the test statistic ($t_{0}$), based on given observations. Reject Ho; to = 1.961 Reject Ho; to = 2.489 Reject Ho; to = 1.432 Fail to reject Ho; to = 1.432