Ch. 2 Review Sheet
- Students in a large psychology class measured the time, in seconds, it took each of them to perform a certain task. The times were later converted to minutes. If a student had a standardized score of z = 1.72 before the conversion, what is the standardized score for the student after the conversion?
(A)z = 0.26
(B)z=1.03
(C)z=1.72
(D)z = 1.98
(E)The standardized score for the student after the conversion cannot be determined.
2.The prices, in thousands of dollars, of 35 used cars at a certain car dealership are shown in the table below.
Which of the following best describes the shape of the distribution of used car prices at the dealership?
(A)Skewed to the left (negatively skewed)
(B)Skewed to the right (positively skewed)
(C)Bimodal
(D)Uniform
(E)Approximately Normal
3.Athletes in a particular sport are classified as either offense or defense. The distribution of weights for the athletes classified as offense are approximately normally distributed, centered at 200 pounds, and ranges from 150 pounds to 250 pounds. The distribution of weights for the athletes classified as defense is approximately normal, centered at 300 pounds, and ranges from 250 pounds to 350 pounds. There are 1,500 athletes in each classification. Which of the following is the best description of the histogram of all 3,000 athletes.
(A)Skewed to the right (positively skewed)
(B)Skewed to the left (negatively skewed)
(C)Approximately Uniform and centered at 250 pounds
(D)Approximately Normal and centered at 250 pounds
(E)Bimodal
- A distribution of scores is approximately normal with a mean of 78 and a standard deviation of 8.6. Which of the following equations can be used to find the score x above which 33 percent of the scores fall?
(A)
(B)
(C)
(D)
(E)
5.The height of 3-year-old boys is approximately normally distributed. Duncan and Shane are 3-year-old boys. Duncan is 32 inches tall and is in the 32nd percentile of the distribution. Shane is 34 inches tall and is at the 62nd percentile of the distribution. Which of the following is closest to the mean of the height distribution?
(A)32.50 inches
(B)32.79 inches
(C)33.00 inches
(D)33.21 inches
(E)36.53 inches
- Height, in meters, is measured for each person in a sample. After the data are collected, all the height measurements are converted from meters to centimeters by multiplying each measurement by 100. Which of the following statistics will remain the same for both units of measure?
(A)The mean of the height measurements.
(B)The median of the height measurements.
(C)The standard deviation of the height measurements.
(D)The maximum of the height measurements.
(E)The z-scores of the height measurements.
7. In a large set of data that are approximately normally distributed,
r is the value in the data set that has a z-score of -1.00,
s is the value of the first quartile, and
t is the value of the 20th percentile.
Which of the following is the correct order from least to greatest for the values or r, s, and t?
(A)r, s, t
(B)r, t, s
(C)s, t, r
(D)t, r, s
(E)t, s, r
8.Each value in the sample has been transformed by multiply by 3 and then adding 10. If the original sample had a variance of 4, what is the variance of the transformed sample?
(A)4
(B)12
(C)16
(D)22
(E)36
9.The distribution of weights of female college cross-country runners is approximately normal with mean of 122 pounds and a standard deviation of 8 pounds. Which of the following is closest to the percent of runners who weigh between 114 pounds and 138 pounds?
(A)18%
(B)32%
(C)68%
(D)82%
(E)95%
10. A distribution of test scores is not symmetric. Which of the following is the best estimate of the z-score of the third quartile?
(A)0.67
(B)0.75
(C)1.00
(D)1.41
(E)The z-score cannot be estimated from the information given.
- In a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. It was determined that the average speed was 42 mph and the standard deviation was 15 mph. In addition, a histogram revealed that vehicle speed at impact is approximately normally distributed.
a)Between what two numbers did the middle 95% of all the recorded speeds fall? Draw a sketch and justify your answer.
b)What proportion of vehicle speeds were between 30 mph and 55 mph? Draw a sketch and justify your answer.
c)What vehicle speed would rank in the 90th percentile? Draw a sketch and justify your answer.
12. A large regional real estate company keeps records of home sales for each of its sales agents. Each month, the company publishes the sales volume for each agent. Monthly sales volume is defined as the total sales price of all homes sold by the agent during a month. The figure below displays the cumulative relative frequency plot of the most recent monthly sales volume (in hundreds of thousands of dollars) for these agents.
(a) In the context of this question, explain what information is conveyed by the circled point.
(b) What proportion of sales agents achieved monthly sales volumes between $700,000 and $800,000? Justify your answer.
(c) For values between 10 and 11 on the horizontal axis, the cumulative relative frequency plot is flat. In the context of this question, explain what this means.
(d) A bonus is to be given to 20 percent of the sales agents. Those who achieved the highest monthly sales volume during the preceding month will receive a bonus. What is the minimum monthly sales volume an agent must have achieved to qualify for the bonus?