Download Chapter 2анаThe Normal DistributionанаReview Game Round

Chapter 2 ­ The Normal Distribution ­ Review Game
Round 1 ­ DO NOT WRITE ON THIS PAPER.
1) The volumes of cola in bottles of certain soft drink brands are normally distributed with a mean of 16 ounces
and a standard deviation of 0.1 ounces. Which of the following intervals represents the middle 40% of this
distribution?
a) 15.98 to 16.02
b) 15.97 to 16.03
c) 15.96 to 16.04
d) 15.95 to 16.05
e) 15.92 to 16.08
2) The students in a college all take a standardized test scored on a scale from 0 to 100 points. The mean and
standard deviation are 53 and 16, respectively. Hugh’s test result has a z­score of 1.19 and Neal’s has a
z­score of 2.06. Neal’s test score is how many points higher than Hugh’s?
a) 0.87
b) 14
c) 19
d) 33
e) 46
3) Which of the following statements is (are) true about normal distributions?
I The mean is the same as the median.
II A normal distribution with standard deviation of 2 has a peak that is higher than a normal distribution
with a standard deviation of 1.
III A normal distribution is completely described by giving its mean and standard deviation.
a) I only
b) II only
c) III only
d) I and III
e) I, II, and III
4) Scores on a standardized test are normally distributed with a mean of 510. Find the standard deviation for
the test scores given that the probability of a score above 600 is 0.32.
a) 42
b) 90
c) 120
d) 132
e) 192
5) The diameters of a certain type of ball bearing are approximately normally distributed with a mean of 2.20 cm
and a standard deviation of 0.02 cm. The largest 1% of all ball bearings will have diameters greater than
a) 2.15 cm
b) 2.20 cm
c) 2.22 cm
d) 2.25 cm
e) 2.29 cm
6) A standardized test has scores that are normally distributed with a mean of 680 and a standard deviation of
25. Approximately what proportion of scores is between 650 and 720?
a) 0.11
b) 0.17
c) 0.38
d) 0.83
e) 0.95
Round 2 ­ DO NOT WRITE ON THIS PAPER.
7) The distribution of students at 20 high schools in a Midwestern city follows an approximate normal
distribution. Twenty percent of the students are less than 55 inches and 10% of the students are more than 62
inches. What are the mean and standard deviation of the distribution of heights of high school students in this
Midwestern city?
a) Mean = 57.8, standard deviation = 3.30
c) Mean = 58.0, standard deviation = 4.76
e) Mean = 59.0, standard deviation = 3.13
b) Mean = 58.0, standard deviation = 3.57
d) Mean = 59.0, standard deviation = 2.34
8) Mary’s best time for downhill skiing the challenging course has a z­score of 0.5 as compared to all skiers that
are timed on the same course. Which statement best interprets her z­score?
a) Mary’s time is 0.5 times faster than all skiers timed on the same course.
b) Mary’s time is 0.5 seconds faster than all skiers timed on the same course.
c) Mary’s time is 0.5 standard deviations below the mean time for all skiers timed on the same course.
d) Mary’s time is 0.5 standard deviation above the mean time for all skiers timed on the same course.
e) Mary skis worse than the majority of the skiers timed on the same course.
9) The weights of young­of­the­year moose are normally distributed with a mean of 430 pounds and a standard
deviation of 42 pounds. Between what two values is the middle half of all young­of­the­year moose weighs?
a) 304 pounds to 556 pounds
b) 346 pounds to 514 pounds
c) 388 pounds to 472 pounds
d) 402 pounds to 458 pounds
e) 409 pounds to 451 pounds
10) A student recently took a standardized mathematics exam to measure academic knowledge. This exam is
used to qualify candidates for admission to a college mathematics program. The student’s exam results were
given as follows:
Raw Score: 45
Percentile: 90
Based on the test results shown, which of the following statements must be true?
a) There were 50 questions on the test.
b) The student answered 90% of the questions correctly.
c) The student scored higher than 90% of all those who took the test.
d) Each question was worth 2 points.
e) There is a 90% chance that the student will be accepted into the math program.
11) A market research company employs a large number of typists to enter data into a computer. The time
taken for new typists to learn the computer system is known to have a normal distribution with a mean of 90
minutes and a standard deviation of 18 minutes. The proportion of new typists that take more than two hours to
learn the computer system is
a) 0.952.
b) 0.548.
c) 0.048.
d) 0.452.
e) 0.7431.
12) A soft­drink machine can be regulated so that it discharges an average of µ ounces per cup. If the ounces
of fill are normally distributed with a standard deviation of 0.4 ounces, what value should µ be set at so that
6­ounce cups will overflow only 2% of the time?
a) 6.82
b) 6.00
c) 5.18
d) 5.60
e) 6.34
Round 3 ­ DO NOT WRITE ON THIS PAPER.
13) Webb is a baseball fanatic. He keeps his own statistics on the major league teams and individual players.
For the 350 regular starters, Webb has found their mean batting average is 0.229, with a standard deviation of
0.024. His sister is appalled that baseball players get paid the salaries they do and get a hit less than 25% of
their attempts at bat. To further her argument, she asks for the following information:
a) What proportion of players hit more than 25% of the times they are at bat?
b) Since the players with the top ten batting averages get cash bonuses, what is the lowest batting average that
will receive a bonus?
ANSWERS
1) D
2) B
3) D
4) E
5) D
6) D
7) A
8) D
9) D
10) C
11) C
12) C
13) (a) z = 0.25−0.229
0.024 = 0.875 0.1922 about 19% of the players get hits on average over 25% of the time. 2 pts.
(b) 10/350 = 0.02857 2.857% get a raise 2 pts.
1 ­ 0.02857 = 0.97143
z = 1.9
x = 0.2746
The top 10 players have batting averages of 0.2746 or higher. 2 pts.