Consider the question of whether the home team wins more than half of its games in the National Basketball Association. Suppose that you study a simple random sample of 80 professional basketball games and find that 52 of them are won by the home team. Assuming that there is no home court advantage and that the home team therefore wins 50% of its games in the long run, determine the probability that the home team would win 65% or more of its games in a simple random sample of 80 games.
A common test for extrasensory perception (ESP) asks subjects to identify which of four shapes (star, circle, wave, or square) appears on a card unseen by the subject. Consider a test of n = 40 trials, where you will count how many times the subject specifies the correct shape. Suppose you want to determine if Chris has ESP. Let p = probability of a correct answer for Chris (that is, the proportion of correct responses if we tested Chris forever). If Chris does not have ESP and is just guessing, what is the value for p?
What is the probability he gets more than 30 correct out of 40 trials?
8. Jack reports he has ESP. To prove it, he states the color (red or black) of a card drawn at random from a deck of 52 cards. He does this for 30 cards (with replacement). Suppose he is correct on 18 of the cards. He states, "See, I got more than half correct? " What do you think? One way of reasoning here is: If Jack is just guessing how odd is it that he gets 18 or more correct out of 30?; i.e., obtain the probability that X ≥ 18.
In a study of hypertension and optimal treatment, 10,005 patients had a mean systolic blood pressure of 161 mm Hg with a standard deviation of 18 mm Hg. Assume systolic blood pressure is normally distributed. Determine the 70th percentile of systolic blood pressure for this group.