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1. Suppose a team of biologists has been studying the Pinedale's Hunting grounds. Let x represent the weight of a single deer taken from the hunting grounds. This group of biologists has determined that x has a normal distribution with mean = 1000kg and standard deviation = 56.6kg.

a) What is the probability that a single deer taken at random from the hunting grounds weighs between 900kg and 1200kg? (6) 2. A certain amount of sugar occurs in every SuperSugarySodaSnack. Let x be mg of sugar (mg). The health department has found that if the SuperSugarySodaSnack does not have too much sugar, then x has a bell-shaped distribution. The mean of the x distribution is = 2000, and the standard deviation is = 250. In a large factory, the health inspector takes 45 random samples of the SuperSugarySodaSnack produced each day. At the end of the day, the sugar level in each of the 45 samples is averaged to obtain the sample mean sugar amount (mg). (16) a) Assuming drinks do not have too much sugar, what is the distribution of ? Hint: Does the central limit theorem apply? Calculate the mean and standard deviation of the distribution. (6) b) Assuming the drinks do not have too much sugar, what is the probability that the average sugar level for one day is between 2450 and 2750 mg sugar? (6) c) If the mean is found to larger than 2750mg sugar/drink, the drinks must be recalled. What does this result tell you given this context? (4)

3. Prisha enjoys writing. She has been writing over a period of several years, during which time her ability to write books has remained quite good. Usually, she writes 5 sheets per day. The standard deviation of her times is = 20.60 minutes. During the past year, Prisha has recorded her times to write 5 sheets. She has a random sample of 80 of these times. For these 80 times, the mean was x = 163.4 minutes. Let be the mean writing time for the entire distribution of Prisha's 5-sheet writing times (taken over the past year). (12) a) Find a 0.95 confidence interval for . Hint: What does a sample size this large help us assume? (6) b) What rule helps you to make an assumption above? Describe this rule in words, briefly (4). Hint: Return to the Sampling Distribution slideshow. (6)

4. State the null hypothesis for the following scenarios. Remember to use proper notation and wording for full marks. (16) a) A bronco rider says the average time he can stay on a bull is 7.36 seconds. He thinks the addition of a new lucky hat will increase his time. b) A zoo records the average number of guests that come, per month, over the course of six months. They claim that an average of 2200 guests come every month to see their zoo. c) A team of basketball players has a mean play time of 5.63 minutes per person. The coach hopes that introducing a new sports energy drink at halftime will allow the players to increase how long they are in the game. d) A nanny believes that the more sleep a baby gets, the less fussy they will be. She lets the baby nap for an average of 5.69 hours a day.