(#2.)

A large shipment of Granny Smith apples arrives at a grocery store. Weights of the apples are known to follow a normal distribution with mean152grams and standard deviation16grams. (a) You select a random sample of three apples. Can you calculate the probability that the mean weight of the apples in the sample is less than141.28?

(b) If you select a random sample of 40 apples, what is the probability that the mean weight of the apples in the sample is between144.89and155.42?

(c) If you select a random sample of 50 apples, what is the probability that the total weight of the apples is greater than7688.25grams?

(d) Are the probabilities you calculated in (b) and (c) exact or approximate? Explain.

(#3.)

Theamount of a waiter's tips follows some right-skewed distribution with mean $6.62and standard deviation $3.55.

(a) We take a random sample of three of the waiter's customers. Can you calculate the probability that the mean tip for these customers isless than $9.43?

(b) If we take a random sample of 35 of the waiter's customers,what is the probability that the mean tip for these customers is greater than $6.13? (c) If we take a random sample of45 of the waiter'scustomers, what is the probability that the mean tip for these customers is between $5.08and $6.87?

(d) Are the probabilities you calculated in (b) and (c) exact or approximate? Explain.

(#4.)

Determine whether the variableXhas a binomial distribution in each of the following cases. If it does, explain why and determine the values of the parametersnandp. If it doesn't, explain why not.

(a) You randomly select one card from each of ten different decks of playing cards. X= number of Clubs selected

(b) You toss five fair coins -- a loonie, a quater, a dime, a nickel and a penny. X= number of coins that land on Heads

(c) You select one row in the random digits Table B from the textbook. X= number of 8's in the row

(d) A fair die is rolled five times. X= number of times the number 3 is observed.

(e) You randomly select one resident of each of the 20 houses on a city block. X= number of females in the sample.

(f)You are dealt a five-card poker hand.

X= number of Diamonds in your hand.

(g) An airplane carrying 100 passengers has two emergency exits -- one at the front of the plane and one over the wings. The plane makes an emergency landing. X= number of passengers that exit the plane through the front emergency exit.

(h) A boy asks the same girl to go on a date every day for a week. X= number of times the girl agrees to go on a date with the boy

(i) A fair die is repeatedly rolled.

(#5.)

m&m's chocolate candies come in six different colours. Suppose the colour distribution is as follows:

Colour	Blue	Brown	Green	Orange	Red	Yellow
Probability	0.12	0.23	0.17	0.16	0.22	0.1

(a) If you randomly select nine m&m's, what is the probability that exactly three of them are brown? (b) If you randomly select 15 m&m's, what is the probability that less than three of them are green? (c) If you randomly select 175 m&m's, what is the approximate probability that at least19% of them are orange? (d) If you randomly select 250 m&m's, what is the approximate probability that between21% and27% of them are red?

(#6.)

*Give all answers to four decimal places. A large lecture theater has230seats,21of which can accomodate left-handed students. Suppose it is known that12% of people are left-handed. One class held in the theater has209students. (a) LetXbe the number of left-handed students in the class. What are the mean and standard deviation ofX? (b) LetP^(P-hat) be theproportion of left-handed students in the class. What are the mean and standard deviation of P^(P-hat) ? (c) What is the approximate probability that all left-handed students in the class get an appropriate desk?