1) Tutors are employed at the Greenville Technical College Math tutoring center on a daily basis. On a normal day when the semester is in full swing, tutors may serve anywhere between 2 and 8 students, inclusive, in one hour.

Suppose the probability that exactly 2 students are served in an hour is 0.094, the probability that exactly 3 students are served is 0.167, the probability that exactly 4 students are served is 0.233, the probability that exactly 5 students are served is 0.217, the probability that exactly 6 students are served is 0.193 and the probability that exactly 8 students are served is 0.024.

Find the probability that exactly 7 students are served in an hour, then construct a probability distribution for this data. (5 points)

2) In the Healthy Handwashing Survey conducted by the Bradley Corporation, 64% of surveyed adults admitted to operating the "flusher" device on public toilets with their foot. Suppose a random sample of 12 adults was selected from the population.

a) List the reasons why this would qualify for a binomial experiment. (4 points)

b) What is the probability that exactly 8 adults in the sample will admit to operating the "flusher" device on a public toilet with their foot. Show your calculation or paste your output from StatCrunch here, for full credit. (3 points)

c) What is the probability that at least 9 adults in the sample will admit to operating the "flusher" device on a public toilet with their foot. Show your calculations or paste your output from StatCrunch here, for full credit. (5 points)

d) What is the mean and standard deviation for this sample? Be sure to show your work for full credit. Give a correct and proper interpretation of the mean. (4 points)

3) Resting heart rates for various age groups tend to follow a normal distribution, with the mean and standard deviation changing as a person ages and moves into different age groupings. For someone between the ages of 18 and 25 years of age, the mean resting heart rate is 72 beats per minute, with a standard deviation of 10 beats per minute. Use this information to answer the following questions.

a) According to the Empirical Rule, what percentage of adults between the ages of 18 and 25 have a resting pulse rate of between 62 and 92 beats per minute? Be sure to show your calculation for this.

b) Using StatCrunch, construct a distribution plot for the percentage of adults between the ages of 18 and 25 having a resting pulse rate of between 62 and 92 beats per minute. Copy and paste this graph into your project document. How does the probability shown for the shaded region in StatCrunch compare with your answer from part (a)? (4 points)

c) Regulations require anyone serving in the U.S. Armed Forces to have a resting heart rate of 100 beats per minute or less. What percentage of adults between the ages of 18 and 25 would be deemed unfit for military service because their resting heart rate was more than 100 beats per minute? Use StatCrunch and paste the graphical display here. What is the associated probability, which accompanies the graph? (5 points)

d) 7% of adults between the ages of 18 and 25 have a resting heart rate above what value? Use StatCrunch to find this probability, and paste the accompanying graph to this project. (5 points)

e) What resting heart rates separate the middle 76% of the population from the rest? Use StatCrunch to find this probability...and paste the graphical output here. (8 points)

4) The average number of pounds of meat that a person consumes per year is 218.4 pounds. Assume that the standard deviation is 25 pounds and the distribution is approximately normal.

a) Find the probability that a person selected at random consumes less than 224 pounds of meat per year. Calculate the z-score manually, and use StatCrunch or the Standard Normal Table to calculate the probability, rounding to four decimal places. (4 points)

b) If a sample of 40 individuals were selected randomly, find the probability that the mean of the sample will be less than 224 pounds per year. Calculate the z-score manually, and use StatCrunch or the Standard Normal Table to calculate the probability, rounded to four decimal places. (4 points)

c) Why are the probabilities in parts (a) and (b) so different? (2 points)

5) In 2017, the city of Burrusville contained 26,898 households. According to city records, 16,275 of these households had a dog. Use this information to answer the following questions.

a) What is p, the population proportion? Show your calculation and round your solution to three decimal places. (2 points)

b) Suppose a simple random sample of 140 homes were chosen at random, and 91 of these homes had a dog. Verify that the sampling distribution is approximately normal. (3 points)

c) What is the probability that a random sample of 140 homes from Burrusville would contain 91 or fewer with a dog? (4 points)