1) Mars Incorporated claims that 14% of its plain m&m candies are yellow. A sample of 100 plain m&m's are selected.

a) Find the mean and standard deviation for the number of yellow candies in such a group of 100.

b) If a group of 100 is found to have 8 yellow candies, is that an unusually low amount?

2) A student is unprepared for a multiple-choice quiz with 10 questions and all their answers are random guesses. Each question has 5 possible answers and only one is correct, so they have one chance in 5 of getting any given question correct.

a) Find the mean and standard deviation for the number of correct answers for such a student.

b) Would it be unusual for this type of guessing student to get at least 7 right? Why or why not?

3) The Central Intelligence Agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages that are sent as ciphered text. In standard English text, the letter h is used at a rate of 6%.

a) Find the mean and standard deviation for the number of times the letter h will be found on a typical page of 2,600 characters.

b) An intercepted page of 2,600 characters is found to have the letter h occurring 128 times. Is 128 unusually low? Show your work.