1. Nutritional data about a sample of seven breakfast includes the number of calories and sugar per serving are shown in the following table. (20 points)
a. Compute the mode, range, median, average, standard deviation for the two sets of data.
b. Compute the Z scores of the two sets of data, is there outlier?
c. Compute the coefficient of variation (CV) of the number of calories for the cereals.
Comparing to the CV of amount of sugar, supposedly 57%, which is more variable?
Cereal Calories Sugar
Kellogg’s All Bran 80 6
Kellogg’s Corn Flakes 100 2
Wheaties 100 4
Nature’s Path Organic
Multigrain Flakes 110 4
Kellogg’s Rice Krispies 130 4
Post Shredded Wheat
Vanilla Almond 190 11
Kellogg’s Mini Wheats 200 10
2. With the data in the previous table. (20 points)
a. Calculate the covariance.
b. Calculate the coefficient of correlation. What conclusions can you reach about the relationship between calories and sugar?
c. Which do you think is more valuable in expressing the relationship between calories and sugar—the covariance or the coefficient of correlation? Explain.
3. The probability that a person has a certain disease is 0.03. Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually present, the probability that the medical diagnostic test will give a positive result (indicating that the disease is present) is 0.90. If the disease is not actually present, the probability of a positive test result (indicating that the disease is present) is 0.02. Suppose that the medical diagnostic test has given a positive result (indicating that the disease is present). What is the probability that the disease is actually present? What is the probability of a positive test result? (10 points)
4. Suppose that 20% of all copies of a particular textbook fail a certain binding strength test. Let
X denote the number among 15 randomly selected copies that fail the test. (20 points)
a. What is the probability that at most 8 fail the test?
b. What is the probability that exactly 8 fail?
c. What is the probability that between 4 and 7 fail?
5. Suppose that blood chloride concentration (mmol/L) has a normal distribution with mean 104 and standard deviation 5. (20 points)
a. What is the probability that chloride concentration equals 105? Is less than 105? Is at most 105?
b. What is the probability that chloride concentration differs from the mean by more than 1 standard deviation? Does this probability depend on the values of population mean µ and population standard deviation s?
c. How would you characterize the most extreme .1% of chloride concentration values?