1. There are 54 skittles in an average 2 oz bag with a standard deviation of 2 skittles. Draw the normal distribution curve (2 points) and answer
the following questions. Show your work.

a. If they tested 3000 bags of skittles, how many of the bags had between 52 and 56 skittles in them? (1 point)

b. If they tested 3500 bags of skittles, how many of the bags had between 54 and 56 skittles in them? (1 point)

c. If they tested 2000 bags of skittles, how many of the bags had between 50 and 56 skittles in them? (1 point)

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?