1. The Normal Distributions
BPS 7e Chapter 3
© 2014 W. H. Freeman and Company

2. Density Curves
Which one of the following is a FALSE statement about density curves?
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 curve is an idealized depiction of the distribution of a variable.

3. Density Curves (answer)
Which one of the following is a FALSE statement about density curves?
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 curve is an idealized depiction of the distribution of a variable.

4. Density Curves
Which one of the following is a FALSE statement about density curves?
The median divides the area under the curve in half.
The mean is the balancing point of the density curve.
The mean and the median are always the same number.

5. Density Curves (answer)
Which one of the following is a FALSE statement about density curves?
The median divides the area under the curve in half.
The mean is the balancing point of the density curve.
The mean and the median are always the same number.

6. Density Curves
If you knew that  = 0 and  = 3, which density curve applies?
Curve 1
Curve 2

7. Density Curves (answer)
If you knew that  = 0 and  = 3, which density curve applies?
Curve 1
Curve 2

8. Density Curves
Here is a density curve as a model for the distribution of spoilage times of a packaged product.
Is the mean spoilage
time smaller than the
median spoilage time?
yes no

9. Describing Density Curves (answer)
Here is a density curve as a model for the distribution of spoilage times of a packaged product.
Is the mean spoilage
time smaller than the
median spoilage time?
yes no

10. Normal Distributions
Here is a normal density curve as a model for the distribution of birth weights of full-term babies in the United States.
True or False:
Baby Emma,
who weighed 4350 g
at birth, was larger
than half of newborn
babies.
True
False

11. Normal Distributions (answer)
Here is a normal density curve as a model for the distribution of birth weights of full-term babies in the United States.
True or False:
Baby Emma,
who weighed 4350 g
at birth, was larger
than half of newborn
babies.
True
False

12. Normal Distributions
Here is a normal density curve as a model for the distribution of birth weights of full-term babies in the United States.
The median full-term
birth weight is 3485 g.
What is mean
full-term birth weight?
less than 3485
equal to 3485
greater than 3485

13. Normal Distributions (answer)
Here is a normal density curve as a model for the distribution of birth weights of full-term babies in the United States.
The median full-term
birth weight is 3485 g.
What is mean
full-term birth weight?
less than 3485
equal to 3485
greater than 3485

14. 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 and 9,000 people in attendance.
68%
95%
99.7%

15. 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 and 9,000 people in attendance.
68%
95%
99.7%

16. Rule
SAT scores follow a normal distribution with mean  = 500 and standard deviation  = Estimate the percentage of SAT scores that have between 300 and 700 points.
68%
95%
99.7%

17. Rule (answer)
SAT scores follow a normal distribution with mean  = 500 and standard deviation  = Estimate the percentage of SAT scores that have between 300 and 700 points.
68%
95%
99.7%

18. Rule
Birth weights of full-term babies in the United States approximately follow the normal distribution with m = 3485 and s = 425.
What percent of
full-term babies have
weights greater than
2635 g?
97.5%
84%
68%
50%

19. Rule (answer)
Birth weights of full-term babies in the United States approximately follow the normal distribution with m = 3485 and s = 425.
What percent of
full-term babies have
weights greater than
2635 g?
97.5%
84%
68%
50%

20. Standard Normal Distribution
Which one of the following is a FALSE statement about the normal distribution?
The mean is greater than the median.
It is symmetric.
It is bell-shaped.
It has one peak.

21. Standard Normal Distribution (answer)
Which one of the following is a FALSE statement about the normal distribution?
The mean is greater than the median.
It is symmetric.
It is bell-shaped.
It has one peak.

22. Standard Normal Distribution
All Normal distributions satisfy the rule, which describes what percent of observations lie within one, two, and five standard deviations of the mean, respectively.
True
False

23. Standard Normal Distribution (answer)
All Normal distributions satisfy the rule, which describes what percent of observations lie within one, two, and five standard deviations of the mean, respectively.
True
False

24. Standard Normal Distribution
Which one of the following is a TRUE statement about the standard Normal distribution?
The standard Normal distribution is the Normal distribution N(0; 1) with mean 0 and standard deviation 1.
The mean and the median are not always the same in standard Normal distributions.
While it mostly has one peak, it can have up to three peaks.
Its mean  is constant at 1.

25. Standard Normal Distribution (answer)
Which one of the following is a TRUE statement about the standard Normal distribution?
The standard Normal distribution is the Normal distribution N(0; 1) with mean 0 and standard deviation 1.
The mean and the median are not always the same in standard Normal distributions.
While it mostly has one peak, it can have up to three peaks.
Its mean  is constant at 1.

26. Standard Normal Distribution
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 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?
Plot A
Plot B

27. Standard Normal Distribution (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 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?
Plot A
Plot B

28. Standard Normal Distribution
Which one of the following is a FALSE statement about a standardized value (z-score)?
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.

29. Standard Normal Distribution (answer)
Which one of the following is a FALSE statement about a standardized value (z-score)?
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.

30. Finding Proportions
What percentage of values of a variable following the standard normal distribution is between z-scores of 0 and 3?
~33.2%
~49.5%
~90.7%
~94.5%

31. Finding Proportions (answer)
What percentage of values of a variable following the standard normal distribution is between z-scores of 0 and 3?
~33.2%
~49.5%
~90.7%
~94.5%

32. Finding Values
Consider a Normal model that describes student scores in a chemistry class. Feyza has a standardized score (z-score) of This means that Feyza
is 2.5 points above average for the class.
is 2.5 standard deviations above average for the class.
has a standard deviation of 2.5.
has a score that is 2.5 times the average for the class.
None of the above.

33. Finding Values (answer)
Consider a Normal model that describes student scores in a chemistry class. Feyza has a standardized score (z-score) of This means that Feyza
is 2.5 points above average for the class.
is 2.5 standard deviations above average for the class.
has a standard deviation of 2.5.
has a score that is 2.5 times the average for the class.
None of the above.