AFM Practice Midterm
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Use a power function to model the data and estimate y for x = 12.
x / y1 / 3
2 / 48
3 / 243
4 / 768
5 / 1,875
6 / 3,888
7 / 7,203
8 / 12,288
a. / 62,208
b. / 43,923
c. / 17,373
d. / 85,683
2. Find a logarithmic function to model the data.
x / y1 / 60
2 / 54
3 / 51
4 / 50
5 / 46
6 / 45
7 / 44
a. / f(x) = 0.93(60.73)x
b. / f(x) = 8.25 - 60.04 ln x
c. / f(x) = 60.04 - 8.25 ln x
d. / f(x) = 60.73(0.95)x
3.Find an exponential function to model the data.
x / y1 / 7
2 / 16
3 / 30
4 / 61
5 / 124
6 / 271
7 / 522
a. / f(x) = -42.8 + 116.4 ln x
b. / f(x) = 116.4 - 42.8 ln x
c. / f(x) = 3.56(2.04)x
d. / f(x) = 2.04(3.56)x
4. Find the linear regression equation for the data according to the given model.
x / y1 / 50
2 / 140
3 / 260
4 / 400
5 / 560
6 / 750
7 / 925
8 / 1130
a. / 1.5x + 3.91
b. / 156.13x - 175.71
c. / 49.79x1.50
d. / 5.48x0.32
5. Find a logistic function to model the data.
x / y / a. / f(x) =0 / 98 / b. / f(x) =
2 / 110 / c. / f(x) = 105.6(1.0155)x
4 / 117 / d. / 105.28 + 8.15 ln x
6 / 121
8 / 123
10 / 124
12 / 125
14 / 126
6. As automobiles age, the average miles traveled per gallon decreases. Determine the regression equation that best models the data.
Age (years) / MPG1 / 35
3 / 34
5 / 33
7 / 31
9 / 28
11 / 26
13 / 23
15 / 18
a. / quadratic
b. / exponential
c. / logarithmic
d. / power
7. Lynn and Dawn tossed a coin 60 times and got heads 33 times. What is the experimental probability of tossing heads using Lynn and Dawn’s results?
a. /b. /
c. /
d. /
8. How many ways can 9 different books be stacked on a shelf?
a) 45 b) 362880 c) 81 d)15120
9.A bookstore offers a collection of books. A student can select from one of 3 algebra books,
one of 8 geometry books, and one of 7 calculus books. How many different possibilities are available for that collection?
a) 716 b) 6 c) 18 d)168
10. How many committees of 3 people can be chosen from a group of 9 people?
a)362880 b)504 c)84 d)45
11. How many ways can the top 4 teams be arranged in a league containing 26 teams?
a) 358,800 b) 104 c) 24 d) 98
12. The table shows the populations (in thousands) during a recent year for a sample of 25 cities. Construct a histogram.
Population (Thousands)154 / 286 / 334 / 182 / 216
281 / 89 / 236 / 273 / 314
342 / 123 / 469 / 389 / 134
225 / 312 / 167 / 243 / 429
269 / 373 / 371 / 412 / 261
13. If a dart hits the target at random, what is the probability that it will land in the shaded region?
a) 1/4 b) 15/16 c) 1/15 d) 1/16
14. Find C(7, 5).
a)35 b)16807 c)21 d) 2520
15. Find the variance and standard deviation of the given set of data to the nearest tenth.
{410, 170, 280, 440, 130, 600, 770}
a) 45,542.9 and 213.4 b) 45,542.9 and 230.5 c) 400 and 213.4 d) 2800 and 230.5
16. Find the standard deviation for the given data.
a) 38 b) 7.6 c) 2.15 d) 2.4
The weights of 830 young deer tagged and weighed in a research study are normally distributed with a mean of 76 pounds and a standard deviation of 2.5 pounds.
17. Approximately how many deer weigh more than 81 pounds?
a)21 b) 79 c) 58 d) 76
18. What percent of deer weigh between 71 and 78.5 pounds? Round your answer to the nearest integer.
a) 28% b) 82% c) 37.5% d)68.9%
19. A grocery store will only accept yellow onions that are at least 2.75 in. in diameter. A grower has a crop of onions with diameters that are normally distributed, with a mean diameter of 3.25 in. and a standard deviation of 0.25 in. What percent of the onions will be accepted by the grocery store?
a) 95.5% b) 50% c) 97.5% d) 2.5%
20. The scores on an exam are normally distributed, with a mean of 74 and a standard deviation of7. What percent of the scores are less than 81?
a) 84% b) 16% c) 74% d) 19%
b)
21. Is the pair of events dependent or independent?
You pick a number between 1000 and 5000. Then you flip a coin.
a) Dependent b) independent
22. Suppose you roll a standard number cube once. Are rolling a 4 and rolling a 3 mutually exclusive events?
a) yes b) no
23. Joey’s sock drawer is unorganized and contains 7 black dress socks, 7 black ankle socks, 6 brown dress socks, and 2 brown ankle socks. What is the probability that Joey will blindly reach into his sock drawer and pull out a sock that is brown or a dress sock?
a) 6/22 b)15/22 c) 8/22 d) 13/22
24. The probability that a dessert sold at a certain cafe contains chocolate is 86%. The probability that a dessert containing chocolate also contains nuts is 30%. Find the probability that a dessert chosen at random contains nuts given that it contains chocolate. Round to the nearest tenth of a percent.
a) 34.9% b) 116% c) 46% d) 25.8%
25) Two urns contain white balls and yellow balls. The first urn contains 9 white balls and 9 yellow balls and the second urn contains 8 white balls and 3 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?
a) 4/11 b) 2/29 c) 17/29 d) 7/16