Density Curves
• Horizontal axis
• Has an area of exactly 1 underneath it
• The overall pattern of a distribution. The area under the
curve and above any interval of values on the horizontal
axis is the proportion of all observations that fall in that
interval.
Density curves
• Mean: the equal-areas point, the point that divides the
area under the curve in half
• Median: the balance point, at which the curve would
balance if it was made out of solid material.
In the 2008 Wimbledon tennis tournament, Rafael Nadal
averaged 115 miles per hour (mph) on his first serves.
Assume that the distributions of his first-serve speeds is
Normal with a mean of 115 mph and a standard
deviation of 6 mph. What percent of Rafael Nadal’s first
serves are between 100 and 110 mph?
According to the heights of the three-year-old females are
approximately Normally distribution with a mean of 94.5
cm and a standard deviation of 4 cm. What is the third
quartile of this distribution?
Variable
Score
N
50
Mean
1045.7
Median
1024.7
Variable
Score
Minimum
628.9
Maximum Q1
1577.1
877.7
TrMean
1041.9
StDev
221.9
SE Mean
31.4
Q3
1219.5
5. Some descriptive statistics for a set of test scores are shown
above. For this test, a certain student has a standardized
score of z = -1.2. What score did this student receive on the
test?
A.
B.
C.
D.
E.
266.28
779.42
1008.02
1083.38
1311.98
25) At a college the scores on the chemistry final exam are
approximately normally distributed, with a mean of 75 and a
standard deviation of 12. The scores on the calculus final
are also approximately normally distributed, with a mean of
80 and a standard deviation of 8. A student scores 81 on the
chemistry final and 84 on the calculus final. Relative to the
students in each respective class, in which subject did this
student do better?
A. The student did better in chemistry.
B. The student did better in calculus.
C. The student did equally well in each course.
D. There is no basis for comparison, since the subjects are
different from each other and are in different departments.
E. There is not enough information for comparison, because
the number of students in each class is not known.
21) A company wanted to determine the health care
costs of its employees. A sample of 25 employees
were interviewed and their medical expenses for the
previous year were determined. Later the company
discovered that the highest medical expense in the
sample was mistakenly recorded as 10 times the
actual amount. However, after correcting the error,
the corrected amount was still greater than or equal
to any other medical expenses in the sample. Which
of the following sample statistics must have remained
the same after the correction was made?
A.
B.
C.
D.
E.
Mean
Median
Mode
Range
Variance
17) Gina’s doctor told her that the standardized score (zscore) for her systolic blood pressure, as compared
to the blood pressure of other women her age, is
1.50. Which of the following is the best interpretation
of this standardized score?
A. Gina’s systolic blood pressure is 150.
B. Gina’s systolic blood pressure is 1.50 standard
deviation above the average systolic blood pressure
of women her age.
C. Gina’s systolic blood pressure is 1.50 above the
average systolic blood pressure of women her age.
D. Gina’s systolic blood pressure is 1.50 times the
average systolic blood pressure for women her age.
E. Only 1.5% of women Gina’s age have a higher
systolic blood pressure than she does.
9. A national achievement test is
administered annually to 3rd graders. The
test has a mean score of 100 and a
standard deviation of 15. If Jane's z-score
is 1.20, what was her score on the test?
(A) 82
(B) 88
(C) 100
(D) 112
(E) 118
34. Molly earned a score of 940 on a
national achievement test. The mean test
score was 850 with a standard deviation of
100. What proportion of students had a
higher score than Molly? (Assume that test
scores are normally distributed.)
(A) 0.10
(B) 0.18
(C) 0.50
(D) 0.82
(E) 0.90
12) The heights of adult women are
approximately normally distributed about a
mean of 65 inches with a standard deviation
of 2 inches. If Rachael is at the 99th
percentile in height for adult women, then her
height, in inches, is closest to
A.
B.
C.
D.
E.
60
62
68
70
74