Imagine that I want to make a 4-step random walk. I am fixed to a single dimension - I can take a step to the left or a step to the right. I will decide the direction I will walk by flipping a coin. If the coin lands heads up (H), I will take a step to the right, and if the coin lands tails up (T), I will take a step to the left. I will toss the coin four times in a row and make note of my final location. How many final locations are possible after four coin tosses

Me max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.

Non-euclidean geometry was discovered when, in seeking cleaner alternatives to the fifth postulate, it was found that the negation could also be true a. true b. false