Achildren clothing manufacturer has 500 yards of material to make shirts and skirts. a shirt requires 0.5 yards of fabric, and a skirt requires 1 yard of fabric. it takes 1 hour to make a shirt and 1.5 hours to make a skirt. the manufacture has 800 hours available to make shirts and skirts.

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?