Focus groups of 15 people are randomly selected to discuss products of the yummy company. it is determined that the mean number (per group) who recognize the yummy brand name is 12.5, and the standard deviation is 0.58. would it be unusual to randomly select 15 people and find that fewer than 9 recognize the yummy brand name?

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?