The Normal Distributions

BPS chapter 3

© 2006 W.H. Freeman and Company

SamplingWhich 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 curvesWhich one of the following is a FALSE statement about density curves?

a) Always on or above the x-axis.

b) Area under the curve within an interval is the proportion of values expected in that interval.

c) Total area under the curve depends on the shape of the curve.

d) The median divides the area under the curve in half.

e) 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) Always on or above the x-axis.

b) Area under the curve within an interval is the proportion of values expected in that interval.

c) Total area under the curve depends on the shape of the curve.

d) The median divides the area under the curve in half.

e) The mean is the balancing point of the density curve.

Density curvesLook at the following density curve. Which would be larger, the

median (M) or the mean ()?

a) M would be larger than .

b) M would be smaller than .

c) 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) M would be larger than .

b) M would be smaller than .

c) M and would be equal.

Standard normal distributionWhich one of the following is a FALSE statement about the standard

normal distribution?

a) The mean is greater than the median.

b) It is symmetric.

c) It is bell-shaped.

d) It has one peak.

Standard normal distribution (answer)Which one of the following is a FALSE statement about the standard

normal distribution?

a) The mean is greater than the median.

b) It is symmetric.

c) It is bell-shaped.

d) It has one peak.

Density curvesIf you knew that the = 0 and = 3, which density curve would match

the data?

a) Dataset 1

b) Dataset 2

Density curves (answer)If you knew that the = 0 and = 3, which density curve would match

the data?

a) Dataset 1

b) Dataset 2

68-95-99.7 ruleAttendance 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) 68%

b) 95%

c) 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) 68%

b) 95%

c) 99.7%

Standard normal distributionWhich one of the following is a FALSE statement about the standard

normal curve?

a) Its standard deviation can vary with different datasets.

b) It is bell-shaped.

c) It is symmetric around 0.

d) Its mean = 0.

Standard normal distribution (answer)Which one of the following is a FALSE statement about the standard

normal curve?

a) Its standard deviation can vary with different datasets.

b) It is bell-shaped.

c) It is symmetric around 0.

d) Its mean = 0.

Z-scoresWhich one of the following is a FALSE statement about a standardized

value (z-score)?

a) It represents how many standard deviations an observation lies from the mean.

b) It represents in which direction an observation lies from the mean.

c) 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) It represents how many standard deviations an observation lies from the mean.

b) It represents in which direction an observation lies from the mean.

c) It is measured in the same units as the variable.

Standard normal curveSuppose 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) Plot A

b) 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) Plot A

b) Plot B

Standardized scoresRachael 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)

b)

670 6002.33

30

600 6702.33

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)

b)

670 6002.33

30

600 6702.33

30