Download Discrete Math Review Ch. 16

Discrete Math
Review Ch. 16
250 students in a math class take the final exam. The scores on the exam have an approximately
normal distribution with center score of 75 and standard deviation of 10.
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1) Find the number of students scoring 75 points or more.
2) Find the average score on the exam.
3) Approximately 95% of the class scored between _____ and _____.
4) Assuming there were no outliers, find the lowest score on the exam.
5) Find the percent of the students who scored between 65 and 75 points.
6) Peter's score on the exam places him in the 16th percentile of the class. Find Peter's score.
7) Carol scored 85 points on the exam. Find the percentile ranking of this score.
8) Find the third quartile of the scores on the exam.
9) Find the standardized value (z-value) corresponding to a score of 95.
10) Find the standardized value (z-value) corresponding to a score of 60.
11) Find the percentage of the test scores with standardized values between -3 and 3.
12) Find the number of students who had test scores with standardized values between -0.675 and 1.
As part of a study, 800 college football players are randomly chosen and their weights taken. The
distribution of the weights is approximately normal. The average weight is 235 pounds and the
standard deviation is 25 pounds.
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13)
14)
15)
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17)
18)
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20)
Of the 800 players approximately how many weighed 210 pounds or less?
Assuming there were no outliers, find the range of weights.
Find the first quartile of the weights.
Approximately how many players weighed over 252 pounds?
A weight of 185 pounds corresponds to a standardized value of _____.
A weight of 300 pounds corresponds to a standardized value of _____.
Approximately how many players had weights between 235 and 252 pounds?
Approximately how many players had weights with standardized values between 1 and 2?
Refer to a normal distribution described by the following figure.
21)
22)
23)
24)
25)
μ = _____
σ = _____
What is the approximate value of Q3?
A data value of 40.5 corresponds to a standardized value of _______.
If the standardized value of x is -1.25, then x = _______
Refer to a normal distribution described by the following figure.
26)
27)
28)
29)
30)
Q1 = _____
σ = _____
Approximately 84% of the data lies below _______
A data value of -70 corresponds to a standardized value of ________
If the standardized value of x is 1.25, then x = _________
The last 80 years, records have been kept of the annual rainfall in the Tasmanian desert. The
distribution of annual rainfall is approximately normal and has no outliers. The minimum of 4.5
inches of rain occurred in 1952; the maximum of 11.7 inches of rain occurred in 1934.
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31) What is the approximate average annual rainfall over the last 80 years?
32) The standard deviation of the rainfall distribution is approximately _______
33) In this part of the world, anything over 10.5 inches of annual rainfall is considered a "wet" year. Of the last
80 years, approximately how many were "wet" ones?
34) Two years ago, the annual rainfall was 7.5 inches. The standardized value corresponding to this rainfall is
approximately ____
35) The third quartile of the rainfall distribution is approximately ____
Solve the Problem.
36) The standard deviation of a normal distribution is σ = 20. What is the interquartile range for this distribution?
KEY
1) 50% of 250 = 125
22) (60.5-44.5)/2 = 8
2) .75
23) 52.5+0.675(8) = 57.9
3) z = -2 to z = 2; 55 and 95
24) (40.5-52.5)/8 = -1.5
4) 75-3(10) = 45
25) -1.25=(x-52.5)/8; x = 42.5
5) z = -1 to z = 0; 34%
26) (Q1+104)/2=50; Q1 = -4
6) z = -1; 75-1(10) = 65
27) 104=50+0.675(σ); σ = 80
7) z = 1; 84th percentile
28) z=1; 50+80 = 130
8) 75+0.675(10) = 82 points
29) (-70-50)/80 = -1.5
9) (95-75)/10 = 2
30) 1.25=(x-50)/80; x = 150
10) (60-75)/10 = -1.5
31) (4.5+11.7)/2 = 8.1 inches
11) 99.7%
32) (11.7-4.5)/6 = 1.2 inches
12) 25%+34%=59% of 250 = 148
33) z=(10.5-8.1)/2=1.2; 2.5% of 80 = 2
13) z = -1; 16% of 800 = 128
34) (7.5-8.1)/1.2 = -0.5
14) 235+3(25); 235-3(25);
35) 8.1+0.675(1.2) = 8.9 inches
310-160 = 150 pounds
15) 235-0.675(25) = 218 pounds
16) 252 = Q3; 25% of 800 = 200
17) (185-235)/25 = -2
18) (300-235)/25 = 2.6
19) 25% of 800 = 200
20) 13.5% of 800 = 108
21) (44.5+60.5)/2 = 52.5
36) 0.675(20)=13.5*2 = 27