Examine the stem plot for us retail gas price in dollars

Question

Question 1. Examine the stem plot for US retail gas price (in dollars per gallon) from May 4, 2012: (You must use proper reasoning when interpreting the stem plot.)

32 | 0

33 | 7 7 7 8 9 9 9 9

34 | 0 0 0 0

35 | 4 8

36 | 0

37 | 9 9 9 9

38 | 4 5 5 5 5 5 6 9 9

39 | 9

40 | 0

• Find the 5 number summary for this stem plot
• An upper outlier would be above what price?

Question 2: Find the z-values that enclose the middle 30% of area under the normal distribution.

Question 3: The following data represents the weights of newborn babies (in pounds):

8.2 7.3 5.4 5.9 9.1 6.5 7.3 7.5 6.6 8.5 6.8 7.5 9.3 7.8 8.7

• Find the mean weight a.
• Find the standard deviation of weights b.­­­­­­­­­­­­­­­­­­­­­
• Find the IQR of the weights c.

Question 4: Christine scored 95 on a math test where the class mean was 84 with standard deviation 8. On the same day she scored 92 on an economics test where the mean was 85 with standard deviation 5. Assume both test distributions were normal. On which test did Christine have the better score compared to the other students in the class? Use statistics to explain your answer.

Question 5: Body temperatures of healthy adults are normally distributed with a mean of 98.6^oF and a standard deviation of 0.73^oF. What is the probability of a healthy adult having a body temperature less than 99.6^oF or greater than 100.6^oF?

Question 6: Suppose that motorist in the Pacific Northwest use a mean of 8.2 gallons of gasoline per week with a standard deviation of 0.47 gallons. Assume that gasoline consumption levels are approximately normally distributed.

• What percentage of PNW drivers use more than 9.0 gallons of gasoline per week?
• What percentage of PNW drivers use an amount of gasoline that differs from the mean by more than 0.5 gallons per week?

Question 7: The volume of oxygen consumed (in liters per minute) while a person is at rest and while he or she is exercising (running on a treadmill) was measured for each of 50 subjects. The goal is to determine if the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below.

• The response variable is:
• The r-value is approximately:

Question 8: Suppose that the mean calorie intake for women is 2050 calories per day, with a standard deviation of 175 calories. Assume that calorie intakes follow a normal distribution. Using the68-95-99.7 rule, what percentage of women consume between 1875 and 2400 calories per day?

Question 9: Suppose that the amount that individuals pay for health insurance per month is normally distributed. If the middle 60% of these individuals pay between $330 and $510 per month, find the mean and standard deviation of this distribution.

• Mean______________
• St. Dev_____________

Question 10: Y = -.483X + 43.169 is a regression line describing the relationship between the average number of fat grams consumed per day, X, and the amount of weight lost (in pounds), Y, over a period of six months. The r-value for this relationship is r = -.958.

• Predict the weight loss for a person who consumed an average of 50 fat grams per day.
• In this situation, what is the meaning of 43.169? ___________________
• Does the r-value of -.958 indicate that the intake of fat grams causes a person to lose weight? Be very specific about your answer.

Question 11: A clerk entering salary data into a company spreadsheet accidentally put an extra "0" in the boss's salary (which is the highest salary in the company), listing it as $2,000,000 instead of $200,000. Explain how this error will affect the following statistics for company payroll and why:

• Mean
• Median
• Standard deviation
• IQR

Question 12: Determine whether the following data represents categorical or quantitative data. (2 pts each)

• Amount of weight gained by each person in a group of college freshman. ______________
• Lengths of the yachts docked at the Beach Harbor Yacht Club _________________
• Bank account PIN numbers _________________
• Total dollar value of all items placed in each safe deposit box at a local bank. ____________
• Letter grades on students' English essays _________________

Question 13: Data collected on the total number of minutes people spent in the local emergency room revealed that patients spent on average 166.9 minutes in the ER, with a standard deviation of 55.4 minutes. Assume that the times collected follow a normal distribution.

• What percentage of the ER patient population spent less than 3 hours there?
• What percentage of the ER patient population spent between 2.5 and 3.5 hours there?
• 20% of the ER patients spent less than what amount of time there?

Question 14: The following scores were obtained on the first Statistics test during Summer quarter:

54,83,84,64,69,93,81,96,72,89,93,68,73,91,90,85,91,75,87,70,77,94,100

• Find the 5-number summary for the data.
• Draw a horizontal box plot for this data, include your scale on the axis below.
• Are there any outliers? If so, identify them.

Question 15: The following chart represents information about the class size in a particular high school and the performance on a state achievement test.

Class size	15	17	18	20	21	24	26	29
Average Test Score	85.3	86.2	85.0	82.7	81.9	78.8	75.3	72.1

• Find the correlation coefficient, r, for this data.
• Find the equation of the regression line for this data.

Bonus: Birth weights in Norway are normally distributed with a mean of 3570 grams.  If 40% of the weights are above 3697 grams, find the standard deviation. (Show work.)