Geo C



AP Stats

Chap 1-6

Practice Test

SOLUTIONS

1. C

2. B

3. C

4. A

5. D

6. C

7. C

8. A

9. E

10. B

11. B

12. C

13. D

14. C

15. C

16. C

17. No. Find the IQR value of 80 by subtracting the Q3 and Q1 values. Multiply this IQR by 1.5

to find the value to be added to Q3 and subtracted from Q1 to find the “fences” for the Outlier Rule. The low fence falls at -90…30 – 120, and the high fence falls at 230…110 + 120. No prices in the survey fall beyond these fence values.

18. The z-score that corresponds with the $31.95 price is -0.76. This means that the advertised

price is only 0.76 standard deviations below the mean. This is not unusually low. Also, $31.95 is slightly above the Q1 value, so over 25% of the phones in he survey cost less than $31.95. This provides more evidence that the price is not unusually low.

19.

Use the mean and SD of the data, 800 and 90, respectively, to find the values at 1, 2, and 3

SDs below and above the mean. These are the six values listed on the Normal model above. The display needs a title, which it has, and the three percentages which are a part of the Normal model are also shown.

20. The first quartile of any data falls at the 25% mark. Using the calculator, the 25% mark has a

corresponding z-score of -0.674. Use this value to “work backwards” to solve for the individual data point at this mark…

-0.674 = (x – 800) / 90

x is roughly 739.2959225

The first quartile of this data contains approximately 740 clients.

21. Using the calculator, the 5th percentile (450 clients) has a corresponding z-score of -1.645 and

the 60th percentile (1085) has a z-score of 0.253. Use these values in the following equation to find the sigma value for this situation:

1085 – 450 = 0.253(sigma) – (-1.645)(sigma)

sigma = 334.5

Use this sigma value in the following equation to find the mew value for this situation:

1085 = mew + (.253)(334.6)

mew = 1000.4

Therefore, the appropriate parameters for this gym owner would be N(1000.4 , 334.6).

22. The z-value corresponding to $125 is calculated as:

z = (125 – 80) / 20 = 2.25.

This is above two standard deviations above the mean, and is located at the 98.8-percentile

mark. Yes, this bill is unusual at this local animal hospital.

23. The Q1 mark of any data always has a z-score of -0.67 (by The Emperical Rule), while the

Q3 mark of any data always has a z-score of 0.67. Particular to this situation, the Q1 and

Q3 values are found here:

Q1…-0.67 = (x – 80) / 20 = 66.6

Q3…0.67 = (x – 80) / 20 = 93.4

The IQR is found as the difference between Q3 and Q1. 93.4 – 66.6 = $26.80.

24. The z-score that would correspond to the 12-ounce mark is found as:

z = (12 – 12.1) / .05 = -2.0

Using the calculator, the z-score of -2.0 relates to the .0228 mark. By setting the machine

to fill the cans with an average of 12.1 ounces with a SD of only 0.05, only 2.28% of the cans will be under-filled.

25. a. A display of three boxplots, one for ABC, one for CBS, and one for NBC, would be

appropriate for showing this data.

b.

Among the top 50 shows for the first half of the 1994-95 television viewing season, NBC

had one more show on the list than ABC did. Although NBC’s mean (13.16) was over a

whole rating point lower than ABC’s (14.36), the standard deviation for NBC was lower (2.77, compared to 3.37) – indicating that the ratings for the NBC shows were more consistent than for the ABC shows. The minimum values for the two networks were nearly the same, while NBC’s IQR was considerably smaller than ABC’s IQR. ABC’s third quartile value of 17.35 is noticeably higher than NBC’s third quartile value of 14.70. Although ABC’s data may be skewed to the right, NBC’s ratings are much more skewed to the right. The second quartile for ABC and the second and third quartiles for NBC appear to be somewhat equal. Neither network had outliers in their data.

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