MGF 1106
Review # 3
Prof Nicoli-Suco
---------------------SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the
probability.
1) Three cards are drawn from a deck. The number of kings is counted.
1)
Answer:
x
0
1
2
3
P(x)
0.7826
0.2042
0.0130
0.0002
Find the mean. Round to the nearest tenth.
2) Value Frequency
13
2
17
4
22
2
27
3
33
3
2)
Answer: 22.7
3) Value Frequency
126
2
174
3
236
4
299
4
366
1
3)
Answer: 234.3
Find the mean for the list of numbers.
4) 20, 9, 26, 20 (Round to the nearest tenth, if necessary.)
Answer: 18.8
1
4)
Find the median for the list of numbers.
5) 5, 7, 11, 21, 34, 40, 46
5)
Answer: 21
6) 10, 23, 39, 49, 62, 73, 80
6)
Answer: 49
Find the mode or modes.
7) 5, 9, 83, 3, 2, 8, 37, 1, 4, 16
7)
Answer: No mode
Find the range for the set of numbers.
8) 5, 16, 4, 13, 11
8)
Answer: 12
9) 30, 39, 18, 46, 59
9)
Answer: 41
10) 118, 464, 220, 592, 415, 250
10)
Answer: 474
Find the standard deviation for the set of numbers.
11) 17, 19, 9, 12, 15, 8, 20, 19, 6
11)
Answer: 5.3
12) 55, 75, 20, 46, 90, 40, 76, 89, 78
12)
Answer: 24.2
2
Find the mode or modes.
13) 20, 37, 46, 37, 49, 37, 49
13)
Answer: 37
14) 81, 53, 32, 53, 29, 81
14)
Answer: 81, 53
Find the expected value for the random variable.
15)
y
P(y)
6
8
10
12
15)
0.4 0.4 0.12 0.08
Answer: 7.76
Find the mean for the list of numbers.
16) 79, 54, 79, 97, 54 (Round to the nearest tenth, if necessary.)
Answer: 72.6
3
16)
Find the mean. Round to the nearest tenth.
17) Value Frequency
13
3
20
2
26
6
27
5
36
1
17)
Answer: 23.9
Find the median for the list of numbers.
18) 2, 10, 24, 25, 32, 50
18)
Answer: 24.5
Find the mode or modes.
19) 98, 74, 32, 74, 29, 98
19)
Answer: 98, 74
Find the range for the set of numbers.
20) 24, 31, 14, 42, 55
20)
Answer: 41
4
Find the standard deviation for the set of numbers.
21) 22, 29, 56, 66, 38, 58, 83, 48, 62
21)
Answer: 19.2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the percent of the area under a normal curve between the mean and the given number of standard deviations from
the mean.
22) 3.01
22)
A) 49.86%
B) 50.13%
C) 99.87%
D) 49.87%
Answer: D
23) -2.91
A) 99.64%
23)
B) 49.82%
C) 99.82%
D) 0.18%
Answer: B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the percent of the total area under the standard normal curve between the given z-scores.
24) z = -2.41 and z = 0.0
24)
Answer: 0.4920
25) z = -1.10 and z = -0.36
25)
Answer: 0.2237
26) z = 0.70 and z = 1.98
26)
Answer: 0.2181
5
A company installs 5000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and
distribution approximated by a normal curve. Find the approximate number of bulbs that can be expected to last the
specified period of time.
27) At least 500 hours
27)
Answer: 2500
28) Less than 500 hours
28)
Answer: 2500
29) Between 500 hours and 675 hours
29)
Answer: 2300
30) Between 540 hours and 780 hours
30)
Answer: 1710
31) Less than 690 hours
31)
Answer: 4857
Solve the equation.
32) 9x - (5x - 1) = 2
Answer:
32)
1
4
33) 4(8x - 1) = 16
Answer:
33)
5
8
6
34) (y - 3) - (y + 6) = 7y
Answer: -
35)
34)
9
7
1
1
(9x - 15) = (10x - 6)
3
2
35)
Answer: -1
36) 3[7m - (6m + 6) + 7] = 6m + 5
Answer: -
36)
2
3
Solve the inequality and graph the solution.
37) 5x - 20 20
37)
Answer: [8, )
38) 9x - 7
4x - 14
Answer:
,-
38)
7
5
7
39) 9 + 5t + 4
4t + 21
39)
Answer: [ 8, )
Find the slope of the line passing through the given pair of points.
40) (9, 3) and (2, 2)
Answer:
40)
1
7
41) (5, 2) and (8, -3)
Answer: -
41)
5
3
42) (1, 7) and (1, 5)
42)
Answer: Not defined
43) (-6, -1) and (8, -1)
43)
Answer: 0
Find the slope of the line.
44) y = 3x - 6
44)
Answer: 3
45) 2x + 5y = 20
45)
2
Answer: 5
8
Find an equation in slope-intercept form (where possible) for the line.
1
46) Through (0, 2), m =
3
Answer: y =
46)
1
x+2
3
47) Through (13, 7), m = -2
47)
Answer: y = -2x + 33
48) Through (5, 0), m = -1
48)
Answer: y = -x + 5
49) Through (-9, 5), perpendicular to 3x - 5y = -52
Answer: y = -
49)
5
x - 10
3
50) Through (-1, 15), parallel to 3x + 8y = 69
Answer: y = -
50)
3
117
x+
8
8
51) Through (-5, 4), m = -5
51)
Answer: y = -5x - 21
9
Solve the inequality and graph the solution.
52) 12x - 14 > 2(5x - 6)
52)
Answer: (1, )
Graph the equation.
53) y = 3x - 4
53)
Answer:
10
54) y = -
1
x+2
2
54)
Answer:
11
55) 5y + 6x = 5
55)
Answer:
12
56) 3y - 2x = 15
56)
Answer:
13
57) 2x + 6y = 10
57)
Answer:
Find an equation in slope-intercept form (where possible) for the line.
58) Through (-5, 8) and (-11, -1)
Answer: y =
58)
3
31
x+
2
2
59) Through (-3, 8), parallel to -7x - 5y = -4
Answer: y = -
59)
7
19
x+
5
5
14
Graph the equation.
60) 3y - 5x = 21
60)
Answer:
Solve the problem.
61) After two years on the job, an engineer's salary was $60,000. After seven years on the job,
her salary was $76,000. Let y represent her salary after x years on the job. Assuming that
the change in her salary over time can be approximated by a straight line, give an equation
for this line in the form y = mx + b.
61)
Answer: y = 3200x + 53,600
62) Suppose that the population of a certain town, in thousands, was 105 in 1990 and 141 in
2002. Assume that the population growth can be approximated by a straight line. Find the
equation of a line which will estimate the population of the town, in thousands, in any
given year since 1990.
Answer: y = 3x + 105 where x is the number of years since 1990
15
62)
63) The cost of owning a home includes both fixed costs and variable utility costs. Assume that
it costs $3031 per month for mortgage and insurance payments and it costs an average of
$4.14 per unit for natural gas, electricity, and water usage. Determine a linear equation that
computes the annual cost of owning this home if x utility units are used.
63)
Answer: y = 4.14x + 36,372
64) The cost of owning a home includes both fixed costs and variable utility costs. Assume that
it costs $3262 per month for mortgage and insurance payments and it costs an average of
$3.27 per unit for natural gas, electricity, and water usage. Determine a linear equation that
computes the annual cost of owning this home if x utility units are used.
64)
Answer: y = 3.27x + 39,144
65) Assume that the sales of a certain appliance dealer can be approximated by a straight line.
Suppose that sales were $12,500 in 1982 and $77,000 in 1987. Let x = 0 represent 1982. Find
the equation giving yearly sales S.
Answer: S = 12,900x + 12,500
16
65)