Aspecial liquid is held in a tank described as (x 2 + y 2 ) ≤ z ≤ 1 in a cartesian coordinate system. assume that the density of the liquid at point (x, y, z) is rho(x, y, z) = (2 − z 2 ), provided that the point is actually in the tank. find the total weight of the liquid by integrating rho dx dy dz.

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?