An airliner carries 100 passengers and has doors with a height of 76 in. heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8in. a. if a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.(round to four decimal places as needed.)

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?