Among the three measures of central tendency (mean, median, and mode), mean is usually the preferred one. However, under some circumstances we might want to use median or mode instead. Briefly describe in what circumstances we want to use median and mode, respectively (at least 1 circumstance for each measure).

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?

An amusement park manager determined that about 23 of all customers would wait in long lines to ride the new roller coaster. which simulation could not be used to answer questions about whether a customer would wait?

Use stokes' theorem to evaluate c f · dr where c is oriented counterclockwise as viewed from above. f(x, y, z) = xyi + 5zj + 7yk, c is the curve of intersection of the plane x + z = 8 and the cylinder x2 + y2 = 81.