PLEASE SHOW ALL YOUR WORK

3. Around Halloween each year the grocery store sells three-pound bags of candy containing a mixture of three different mini-bars: Snickers, Milky Way, and Twix. If the bag has an equal number of each of the three bars, then what are the probabilities for each of the following?

a. Randomly selecting a Milky Way bar

b. Randomly selecting either a Snickers or a Twix bar

c. Randomly selecting something other than a Twix bar

5. Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body.

a. z 5 2.00

b. z 5 0.75

c. z 5 21.40

d. z 5 20.67

7 Draw a vertical line through a normal distribution for each of the following z-score locations. Find the proportion of the distribution located between the mean and the z-score.

a. z 5 1.80

b. z 5 0.55

c. z 5 21.10

d. z 5 20.85

9. What proportion of a normal distribution is located between each of the following z-score boundaries?

a. z 5 20.50 and z 5 10.50

b. z 5 20.85 and z 5 10.85

c. z 5 21.60 and z 5 11.60

13. A normal distribution has a mean of m 5 90 and a standard deviation of s 5 15. For each of the following scores, indicate whether the tail is to the right or left of the score and find the proportion of the distribution located in the tail.

a. X 5 93

b. X 5 110

c. X 5 85

d. X 5 70

15. For a normal distribution with a mean of m 5 85 and a standard deviation of s 5 20, find the proportion of the population corresponding to each of the following.

a. Scores greater than 89

b. Scores less than 72 c. Scores between 70 and 100

16. In 2014, the New York Yankees had a team batting average of m 5 245 (actually 0.245 but we will avoid the decimals). Of course, the batting average varies from game to game, but assuming that the distribution of batting averages for 162 games is normal with a standard deviation of s 5 40 points, answer each of the following.

a. If you randomly select one game from 2014, what is the probability that the team batting average was over 300?

b. If you randomly select one game from 2014, what is the probability that the team batting average was under 200?

17. IQ test scores are standardized to produce a normal distribution with a mean of m 5 100 and a standard deviation of s 515. Find the proportion of the population in each of the following IQ categories.

a. Genius or near genius: IQ over 140

b. Very superior intelligence: IQ from 120 to 140

c. Average or normal intelligence: IQ from 90 to 109

19. According to a recent report, the average American consumes 22.7 teaspoons of sugar each day (National Geographic Magazine, August 2013). Assuming that the distribution is approximately normal with a standard deviation of s 5 4.5, find each of the following values.

a. What proportion of people consume more than 30 teaspoons of sugar a day?

b. What proportion of people consume at least 20 teaspoons of sugar a day?

21. A report in 2010 indicates that Americans between the ages of 8 and 18 spend an average of m 5 7.5 hours per day using some sort of electronic device such as smart phones, computers, or tablets. Assume that the distribution of times is normal with a standard deviation of s 5 2.5 hours and find the following values.

a. What is the probability of selecting an individual who uses electronic devices more than 9 hours a day?

b. What proportion of 8- to 18-year-old Americans spend between 8 and 12 hours per day using electronic devices? In symbols, p(8 , X , 12) 5 ?