The table at right contains the weights (measured in pounds) of the ten
most recently delivered babies at a local hospital.
PRACTICE
(1) Draw the normal distribution for this data. Include
dotted line to represent the mean and each standard
deviation. Label each line with the weight it represents.
(2) In terms of standard deviation, how would you say
a baby weighing 8.9 pounds compares to the mean?
________________________
BABY WEIGHTS (IN LBS)
7.4
8.1
9.3
8.4
5.1
7.0
7.5
6.6
9.8
6.8
(3) How would you say a baby weighing 9 pounds compares to the mean? __________________________
WHAT IT IS:
ITS EQUATION:
Z-SCORE
PRACTICE
Consider the table of baby weights above.
(4) Use the z-score equation to prove that a baby weighing
8.9 pounds is one standard deviation above the mean.
PROOF:
(5) Determine exactly how far from the
mean a baby weighing 9 pounds would be. ___________________
(6) Determine the z-score for each baby weight below.
(a) 6 pounds
(b) 7.5 pounds
(c) 11 pounds
(d) 3.2 pounds
_________
_________
_________
_________
(7) What is the approximate probability that the next
baby born at the hospital weighs less than 9 pounds? ____________
(8) Why can’t we use the empirical rule
to find an exact answer to answer #7?
____________________________________________________
(9) Use the z-table to determine the probability that a new baby is born at each weight below.
(a) 6 pounds
(b) 7.5 pounds
(c) 11 pounds
(d) 3.2 pounds
_________
_________
_________
_________
PRACTICE
A professional soccer team is planning to sign one additional player before the season
begins. They are considering adding a goalie or a forward. The goalie has a 90% save percentage, and
the forward averages 1.2 goals per game. The average goalie in the soccer league saves 86% of shots
with a standard deviation of 5%, while the average forward scores 0.9 goals per game with a standard
deviation of 0.2.
(10) Make a hypothesis: which
player is better at his position? _____________
(11) Use z-scores to determine
which player the team should sign.
Why? ________________________________________
_____________
___________
BETTER PLAYER
# OF SD ABOVE PLAYER MEAN
PRACTICE
Mrs. Fibberbibber has assigned three projects to her World Civ class. Antoine, a student in
the class, got the following scores on each project:
A score of 144 on Project #1 with a mean class score of 128 and a standard deviation of 34
A score of 90 on Project #2 with a mean class score of 86 and a standard deviation of 18
A score of 18 on Project #3 with a mean class score of 15 and a standard deviation of 5
(12) Determine the z-score of each project score.
____________
____________
PROJECT #1
____________
PROJECT #2
PROJECT #3
(13) On which project did Antoine do the worst, compared to the rest of his class? ______________
(14) A highly selective university will only admit students who
place at least two z-scores above the mean on the ACT. On the most recent
ACT, the mean score was 18 with a standard deviation of 6. What is the
minimum score that an applicant must obtain to be admitted to the university? ____________
PRACTICE
(15) A pharmaceutical company wants to test a new cholesterol
drug. The average cholesterol of the population is 200 mg with a standard
deviation of 25 mg. The company wishes to test a sample of people who fall
between 1.5 and 3 z-scores above the mean. Into what range must a candidate’s cholesterol level be in order for the candidate to be included in the study? __________________
PRACTICE
PRACTICE
At a local college, the average male student has a height of 69 inches with a standard
deviation of 3”. The average female student has a height of 64” with a standard deviation of 2.5”.
(16) Who is taller, relatively speaking:
a 72” tall male or a 67” tall female?
PROVE IT:
____________
(17) Tall Club International is an organization that caters to exceptionally tall individuals. The height requirement for women to join
TCI is 72 inches. What is the equivalent height requirement for men?
_________
(18) How many standard deviations above the college mean would a
female college student have to be in order to be eligible to join TCI? _________
PRACTICE
In a recent study of IQ scores, the average American had an IQ of 100 with a standard
deviation of 16.
(19) What is the probability that a randomly selected American has an IQ less than 116? _________
(20) What is the probability that a randomly selected American has an IQ greater than 116? _________
PROVE IT:
(21) Albert Einstein reportedly had an IQ of 160.
(a) How many standard deviations above the mean was Einstein’s IQ? _________
(b) Convert Einstein’s IQ score to a z-score. _________
(c) IQ experts consider the typical intelligence range to contain z-scores
between —2 and 2. By this metric, how would you describe Einstein’s IQ? __________________
Consider the histograms shown at right.
REVIEW
SET A
SET B
12
8
4
(22) Which of the histograms represents the
data set with the largest standard deviation? _______
12
8
4
1 2 3 4 5 6 7
1 2 3 4 5 6 7
Why? ____________________________________________
SET D
SET C
(23) Which of the histograms contains data that
would best be represented by the set’s median? _______
12
8
4
12
8
4
Why? ____________________________________________
1 2 3 4 5 6 7
1 2 3 4 5 6 7
REVIEW
(24) During an Anatomy lab, Mary measured the heights (in feet) of 50 students on campus
and recorded the data. She found that the mean height was 5.8 feet with a standard deviation of 0.6
feet. However, when she re-read the lab instructions, she noticed that the measurements were
supposed to be recorded in inches. If she converts her data from feet to inches, which of the
following statements will be true about her results?
THE MEAN WILL INCREASE
THE MEDIAN WILL INCREASE
THE MODE WILL INCREASE
THE STANDARD DEVIATION WILL INCREASE
THE RANGE WILL INCREASE
THE SPREAD OF THE DATA WILL INCREASE
THE CENTER OF THE DATA WILL INCREASE
REVIEW
(25) Mrs. Scuffletuffle works for a car manufacturer. Yesterday she
collected data on the fuel efficiency of nine new cars, measured in miles per
gallon. She found that the mean was 33.6 mi/gal. Today, she revisited her
notes but realized that she only wrote down eight pieces of data: {27, 28, 30,
32, 37, 38, 38, 41}. What was the value of the piece of data she forgot to record?
_________
REVIEW
Find the area of the shaded region represented by each standard normal distribution with
mean 0 and standard deviation 1.
(26)
AREA=________
(27)
AREA=________
–2
–1
(28)
AREA=________
y
y
1
2
x
–2
–1
(29) AREA=________
y
y
1
2
x
–2
–1
1
2
x
–2
–1
1
2
x
REVIEW
For an AP Stats assignment, Mr. DuPont asks his students to perform 1000 trials
of an experiment in which students roll a die and record the number of dots on the face
that lands up. The data is used to generate a histogram similar to that pictured at right.
(30) If the die is far, what shape will the resulting histogram have?
a) normal
b) skewed right
c) skewed left
1 2 3 4 5 6
# OF DOTS ON FACE
d) uniform
(31) If the die is weighted so that the face with one dot is twice as likely to appear as any other face,
what shape will the resulting histogram have?
a) normal
b) skewed right
c) skewed left
d) uniform