1. Which of the following variables is categorical?
2. A professor records the values of several variables for each student in her class. These include the variables listed below. Which of these variables is categorical?
3. This is a histogram of measurements of the length of the textbook for a statistics course using a crude ruler by students in a Spring, 1992 statistics class at Ohio State University. 167 students participated, each having ten friends also give measurements.
The shape of the above histogram is best described as which of the following?
4. Regarding the above histogram, which of the following statements is true?
5. Which of the options best describes the following histogram?
6. Here is a histogram of the gold medal winning high jumps for the Olympic Games:
The center of the above histogram is approximately how many inches?
7. In the above histogram, what is the approximate percentage of the winning jumps that were at least 7 feet (84 inches)?
8. A purchasing agent tests samples of 10 batteries for hand calculators from a certain manufacturer. Each battery is tested in a calculator that is programmed to do a continuous "loop" of typical calculations; the time in hours to failure of each battery is recorded in the table below. Times 11.80 11.91 11.95 12.00 12.02 12.03 12.04 12.07 12.13 12.20 Which of the following is a proper stemplot of these data?
9. Concern over global warming has been much in the news in recent years, especially when we experience unusual weather. In order to determine if global warming has occurred in the past and what its effects were, geologists take soil core samples. These samples are columns of soil extracted from the earth in regions that have been undisturbed by man. Examples of such regions are lake beds in Alaska or Siberia. The depth of a particular portion of the core is proportional to its age. The exact age is estimated by carbon dating. Deeper samples represent more ancient periods. At regular intervals, soil from the core is analyzed for the presence of certain types of plant pollen. In this way, geologists can determine the types and relative quantities of plants present. Dramatic changes may indicate major climate changes.
A timeplot of the amount of eucalyptus pollen using depth of sample as a measure of time, with the core sample from a study sponsored by the Byrd Polar Institute at the Ohio State University. We assume the time scale is uniform in depth.
Based on the above time plot, at which of the following depths does a dramatic change in the amount of eucalyptus pollen appear to occur (note this may indicate a dramatic change in climate occurred)?
10. In a class of 100 students, the grades on a statistics test are summarized on the following frequency table: Grade Frequency 91-100 11 81-90 31 71-80 42 61-70 16 In which of the following intervals is the median grade?
11. A set of data has a median which is much larger than the mean. Which of the following statements is most consistent with this information?
12. For the following histogram, which statement is true?
13. The variance of 10 measurements of people's height (in inches) is computed to be 25. What is the standard deviation of these measurements?
14. What is the standard deviation of the three numbers 4, 1, 1?
15. Consider the following density curve:
Which statement is true?
16. Items produced by a manufacturing process are supposed to weigh 90 grams. The manufacturing process is such, however, that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of weights can be approximated by a normal distribution with mean 90 grams and a standard deviation of 1 gram.
What percentage of the items will either weigh less than 87 grams or more than 93 grams?
17. Using the standard normal distribution tables, what is the area under the standard normal curve corresponding to Z < 2.85?
18. What is the area under the standard normal curve corresponding to Z < -1.44?
19. What is the area under the standard normal curve corresponding to -0.3 < Z < 1.6?
20. What is the area under the normal curve with mean 6 and variance 81 corresponding to 1 < X < 10?
21. The daily cost of running the air conditioner in an office building is approximately normally distributed with a mean of $120 and a standard deviation of $20. What is the proportion of days on which the cost of running the air conditioner is less than $95?
22. The distribution of actual weights of 8 oz. chocolate bars produced by a certain machine is normal with mean 8.1 ounces and standard deviation 0.1 ounces. What is the proportion of chocolate bars weighing under 8 ounces?
23. The distribution of actual weights of 8 oz. chocolate bars produced by a certain machine is normal with mean 8.1 ounces and standard deviation 0.1 ounces. What is the proportion of chocolate bars with weights between 8.2 and 8.3 ounces?
24. Let X denote the time taken for a computer link to be made between the terminal in an executive's office and the computer at a remote factory site. It is known that X has a normal distribution with mean 15 seconds and standard deviation 3 seconds. On 90% of the occasions the computer link is made in less than _______ seconds.
25. The time taken to prepare the envelopes to mail the weekly report to all executives in the company has a normal distribution with mean 35 minutes and standard deviation 2 minutes. On 95% of occasions the mailing preparation takes less than _______ minutes.
26. A soft-drink machine can be regulated so that it discharges an average of m ounces per cup. If the ounces of fill are normally distributed with standard deviation 0.4 ounces, what value should m be set at so that 6-ounce cups will overflow only 2% of the time?
27. The weights of packets of cookies produced by a certain manufacturer have a normal distribution with mean 202 g and standard deviation 3 g. What is the weight that should be stamped on the packet so that only 1% of packets are underweight?
28. A stemplot of a set of data is roughly symmetric, but the data do not even approximately follow the 68 - 95 - 99.7 rule. Which statement best describes the data?
29. The lifetime of a 2 volt non-rechargeable battery in constant use has a normal distribution with mean 516 hours and standard deviation 30 hours. 90% of all batteries have a lifetime of _______ hours.
30. A company produces packets of soap powder which are labeled "GIANT SIZE 32 OUNCES". The actual weight of soap powder in a box has a normal distribution with mean 33 oz. and standard deviation 0.7 oz. 95% of packets actually contain more than x ounces of soap powder. What is x?