The Normal Distributions
BPS chapter 3
© 2006 W.H. Freeman and Company
Sampling
Which of the following quantities would give us information about a
sample?
a)

b)
p
c)

d)
x
Sampling (answer)
Which of the following quantities would give us information about a
sample?
a)

b)
p
c)

d)
x
Density curves
Which one of the following is a FALSE statement about density curves?
a)
b)
c)
d)
e)
Always on or above the x-axis.
Area under the curve within an interval is the proportion of values
expected in that interval.
Total area under the curve depends on the shape of the curve.
The median divides the area under the curve in half.
The mean is the balancing point of the density curve.
Density curves (answer)
Which one of the following is a FALSE statement about density curves?
a)
b)
c)
d)
e)
Always on or above the x-axis.
Area under the curve within an interval is the proportion of values
expected in that interval.
Total area under the curve depends on the shape of the curve.
The median divides the area under the curve in half.
The mean is the balancing point of the density curve.
Density curves
Look at the following density curve. Which would be larger, the
median (M) or the mean ()?
a)
b)
c)
M would be larger than .
M would be smaller than .
M and  would be equal.
Density curves (answer)
Look at the following density curve. Which would be larger, the
median (M) or the mean ()?
a)
b)
c)
M would be larger than .
M would be smaller than .
M and  would be equal.
Standard normal distribution
Which one of the following is a FALSE statement about the standard
normal distribution?
a)
b)
c)
d)
The mean is greater than the median.
It is symmetric.
It is bell-shaped.
It has one peak.
Standard normal distribution (answer)
Which one of the following is a FALSE statement about the standard
normal distribution?
a)
b)
c)
d)
The mean is greater than the median.
It is symmetric.
It is bell-shaped.
It has one peak.
Density curves
If you knew that the  = 0 and  = 3, which density curve would match
the data?
a)
b)
Dataset 1
Dataset 2
Density curves (answer)
If you knew that the  = 0 and  = 3, which density curve would match
the data?
a)
b)
Dataset 1
Dataset 2
68-95-99.7 rule
Attendance at a university’s basketball games follows a normal
distribution with mean  = 8,000 and standard deviation  = 1,000.
Estimate the percentage of games that have between 7,000 to
9,000 people in attendance.
a)
b)
c)
68%
95%
99.7%
68-95-99.7 rule (answer)
Attendance at a university’s basketball games follows a normal
distribution with mean  = 8,000 and standard deviation  = 1,000.
Estimate the percentage of games that have between 7,000 to
9,000 people in attendance.
a)
b)
c)
68%
95%
99.7%
Standard normal distribution
Which one of the following is a FALSE statement about the standard
normal curve?
a)
b)
c)
d)
Its standard deviation  can vary with different datasets.
It is bell-shaped.
It is symmetric around 0.
Its mean  = 0.
Standard normal distribution (answer)
Which one of the following is a FALSE statement about the standard
normal curve?
a)
b)
c)
d)
Its standard deviation  can vary with different datasets.
It is bell-shaped.
It is symmetric around 0.
Its mean  = 0.
Z-scores
Which one of the following is a FALSE statement about a standardized
value (z-score)?
a)
b)
c)
It represents how many standard deviations an observation lies
from the mean.
It represents in which direction an observation lies from the mean.
It is measured in the same units as the variable.
Z-scores (answer)
Which one of the following is a FALSE statement about a standardized
value (z-score)?
a)
b)
c)
It represents how many standard deviations an observation lies
from the mean.
It represents in which direction an observation lies from the mean.
It is measured in the same units as the variable.
Standard normal curve
Suppose the lengths of sport-utility vehicles (SUV) are normally distributed with
mean  = 190 inches and standard deviation  = 5 inches. Marshall just
bought a brand-new SUV that is 194.5 inches long and he is interested in
knowing what percentage of SUVs is longer than his. Using his statistical
knowledge, he drew a normal curve and labeled the appropriate area of
interest. Which picture best represents what Marshall drew?
a)
b)
Plot A
Plot B
Standard normal curve (answer)
Suppose the lengths of sport-utility vehicles (SUV) are normally distributed with
mean  = 190 inches and standard deviation  = 5 inches. Marshall just
bought a brand-new SUV that is 194.5 inches long and he is interested in
knowing what percentage of SUVs is longer than his. Using his statistical
knowledge, he drew a normal curve and labeled the appropriate area of
interest. Which picture best represents what Marshall drew?
a)
b)
Plot A
Plot B
Standardized scores
Rachael got a 670 on the analytical portion of the Graduate Record
Exam (GRE). If GRE scores are normally distributed and have
mean  = 600 and standard deviation  = 30, what is her
standardized score?
a)
670  600
 2.33
30
b)
600  670
 2.33
30
Standardized scores (answer)
Rachael got a 670 on the analytical portion of the Graduate Record
Exam (GRE). If GRE scores are normally distributed and have
mean  = 600 and standard deviation  = 30, what is her
standardized score?
a)
670  600
 2.33
30
b)
600  670
 2.33
30