Question 1

μ = 15.2,15.87% above 16.1;σ = ?

Accepted Answer

A) 1.35 
B) 0.83 
C) 1.25 
D) 0.90 
E) 1.80 
A) 1.35 
B) 0.83 
C) 1.25 
D) 0.90 
E) 1.80

Question 2

The average weight of a newborn infant is 2.7 kg.An infant that ways 3.15 kg has a z-score of 1.Find the standard deviation.

Accepted Answer

A) 0.05 kg 
B) 0.14 kg 
C) 1.35 kg 
D) 0.45 kg 
E) 2.7 kg 
A) 0.05 kg 
B) 0.14 kg 
C) 1.35 kg 
D) 0.45 kg 
E) 2.7 kg

Question 3

A town's average snowfall is 40 cm per year with a standard deviation of 5 cm.According to the Normal model,what percent of snowfall is less than 3 standard deviations from the mean?

Accepted Answer

A) 15.87% 
B) 99.74% 
C) 5% 
D) 2.28% 
E) 0.26% 
A) 15.87% 
B) 99.74% 
C) 5% 
D) 2.28% 
E) 0.26%

Question 4

A bank's loan officer rates applicants for credit.The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50.If an applicant is randomly selected,what percentage can be expected to be between 200 and 275?

Accepted Answer

A) 6.68% 
B) 43.32% 
C) 93.32% 
D) 42.37% 
E) 5.00% 
A) 6.68% 
B) 43.32% 
C) 93.32% 
D) 42.37% 
E) 5.00%

Question 5

The freethrow percentages for the participants of a basketball tournament were compiled.The percents ranged from 39% to 99% with a mean of 50% and a standard deviation of 5%.The quartiles and median percentages were 49%,87%,and 50%.Suppose one participant did not make any of his attempted freethrows (0%).Which of the summary statistics might not change if that data value was added to the distribution?

Accepted Answer

A) Q1,Q3 
B) Mean,IQR 
C) Median,IQR 
D) Range,SD 
E) Median,range 
A) Q1,Q3 
B) Mean,IQR 
C) Median,IQR 
D) Range,SD 
E) Median,range

Question 6

Here are the weekly winnings for several local poker players: $100,$50,$125,$75,$80,$60,$110,$150,$300,$700,$115,$75,$1000,$5000.Which is a better summary of the scores,the mean or the median? Explain.

Accepted Answer

A) Mean,the data is extremely skewed to the left 
B) Median,the data is extremely skewed to the left 
C) Mean,the data is extremely skewed to the right 
D) Median,the data is extremely skewed to the right 
E) Either,the data is symmetric 
A) Mean,the data is extremely skewed to the left 
B) Median,the data is extremely skewed to the left 
C) Mean,the data is extremely skewed to the right 
D) Median,the data is extremely skewed to the right 
E) Either,the data is symmetric

Question 7

the lowest 40%

Accepted Answer

A) 0.50 
B) 0.57 
C) -0.57 
D) 0.25 
E) -0.25 
A) 0.50 
B) 0.57 
C) -0.57 
D) 0.25 
E) -0.25

Question 8

The test scores from a recent Mathematics test are as follows: 95.5,65.9,93.2,88.6,56.8,50,86.4,54.5,40.9,77.3,79.5,65.9,70.5,77.3,81.8,50,79.5,and 68.2.The mean score was 71.2 with a standard deviation of 15.5.If the Normal model is appropriate,what percent of the scores will be greater than 86.7?

Accepted Answer

A) 15.87% 
B) 0.15% 
C) 10% 
D) 34% 
E) 2.28% 
A) 15.87% 
B) 0.15% 
C) 10% 
D) 34% 
E) 2.28%

Question 9

Here are some statistics for the annual Wildcat golf tournament: lowest score = 58,mean score = 97,median = 105,range = 92,IQR = 105,Q1 = 39,standard deviation = 16.Between what two values are the middle 50% of the scores found?

Accepted Answer

A) 26.25 and 78.75 
B) 58 and 150 
C) 39 and 144 
D) 24.25 and 67.9 
E) 97 and 105 
A) 26.25 and 78.75 
B) 58 and 150 
C) 39 and 144 
D) 24.25 and 67.9 
E) 97 and 105

Question 10

The average number of babies born in a certain town each year is 218 with a standard deviation of 26.How many standard deviations from the mean is a year with 387 babies born?

Accepted Answer

A) 3.25 standard deviations below the mean 
B) 6.50 standard deviations above the mean 
C) 3.25 standard deviations above the mean 
D) 6.50 standard deviations below the mean 
E) 1.78 standard deviations above the mean 
A) 3.25 standard deviations below the mean 
B) 6.50 standard deviations above the mean 
C) 3.25 standard deviations above the mean 
D) 6.50 standard deviations below the mean 
E) 1.78 standard deviations above the mean

Question 11

Here are some summary statistics for last years basketball team scoring output: lowest score = 18 points,mean = 58 points,median = 52 points,range = 97 points,IQR = 46,Q1 = 23,standard
Deviation = 9 points.Suppose the opponents' scoring output was 10% lower.Find the opponents' mean and standard deviation.

Accepted Answer

A) Mean: 52.2 points,SD: 8.1 points 
B) Mean: 52.2 points,SD: 9 points 
C) Mean: 63.8 points,SD: 9.9 points 
D) Mean: 63.8 points,SD: 9 points 
E) Mean: 5.8 points,SD: 0.9 points 
A) Mean: 52.2 points,SD: 8.1 points 
B) Mean: 52.2 points,SD: 9 points 
C) Mean: 63.8 points,SD: 9.9 points 
D) Mean: 63.8 points,SD: 9 points 
E) Mean: 5.8 points,SD: 0.9 points

Question 12

Based on the Normal model for snowfall in a certain town N(57,8),how many cm of snow would represent the 25th percentile?

Accepted Answer

A) 51.6 cm 
B) 65 cm 
C) 49 cm 
D) 62.4 cm 
E) 14.3 cm 
A) 51.6 cm 
B) 65 cm 
C) 49 cm 
D) 62.4 cm 
E) 14.3 cm

Question 13

Assuming a Normal model applies,a town's average annual snowfall (in cm)is modeled by N(42,8).Draw and label the Normal model.Then find the interval for the middle 95% of snowfall.

Accepted Answer

A) 
 
;18 to 50 
B) 
 
;34 to 50 
C) 
 
;26 to 58 
D) 
 
;34 to 66 
E) 
 
;18 to 66 
A) 
 
;18 to 50 
B) 
 
;34 to 50 
C) 
 
;26 to 58 
D) 
 
;34 to 66 
E) 
 
;18 to 66

Question 14

the middle 96%

Accepted Answer

A) 0 to 2.05 
B) -2.33 to 2.33 
C) -3.00 to 3.00 
D) -1.75 to 1.75 
E) -2.05 to 2.05 
A) 0 to 2.05 
B) -2.33 to 2.33 
C) -3.00 to 3.00 
D) -1.75 to 1.75 
E) -2.05 to 2.05

Question 15

Here are some summary statistics for the size of forest fires last year: smallest fire = 74 acres,mean = 451 acres,median = 451 acres,range = 7,926 acres,IQR = 387,Q1 = 180,standard deviation = 61 acres.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

Accepted Answer

A) Skewed to the right,mean higher than median. 
B) Symmetric,mean same as median. 
C) Skewed to the left,mean higher than median. 
D) Skewed to the right,mean lower than median. 
E) Skewed to the left,mean lower than median. 
A) Skewed to the right,mean higher than median. 
B) Symmetric,mean same as median. 
C) Skewed to the left,mean higher than median. 
D) Skewed to the right,mean lower than median. 
E) Skewed to the left,mean lower than median.

Question 16

For a recent English exam,use the Normal model N(73,9.2)to find the score that represents the 60th percentile.

Accepted Answer

A) 75.3 
B) 70.7 
C) 82.2 
D) 63.8 
E) 43.8 
A) 75.3 
B) 70.7 
C) 82.2 
D) 63.8 
E) 43.8

Question 17

The scores for a recent English exam can be represented by the Normal model N(67,6.3).What score would you expect to be unusually low for this exam?

Accepted Answer

A) 85.9 
B) 63.85 
C) 73.3 
D) 48.1 
E) 60.7 
A) 85.9 
B) 63.85 
C) 73.3 
D) 48.1 
E) 60.7

Question 18

The annual snowfall in a town (in cm)can be represented by the Normal model N(45,7.1).What amount of snowfall would you expect to be unusually high for this town?

Accepted Answer

A) 48.55 cm 
B) 37.9 cm 
C) 23.7 cm 
D) 66.3 cm 
E) 52.1 cm 
A) 48.55 cm 
B) 37.9 cm 
C) 23.7 cm 
D) 66.3 cm 
E) 52.1 cm

Question 19

Based on the Normal model for snowfall in a certain town N(57,8),how many cm of snow would represent the 85th percentile?

Accepted Answer

A) 49 cm 
B) 48.5 cm 
C) 65 cm 
D) 65.3 cm 
E) 48.7 cm 
A) 49 cm 
B) 48.5 cm 
C) 65 cm 
D) 65.3 cm 
E) 48.7 cm

Question 20

Based on the Normal model for car speeds (in km/h)on a road N(77,9.1),what are the cutoff values for the middle 70% of the speeds?

Accepted Answer

A) about 60.2 km/h,about 93.7 km/h 
B) about 70.2 km/h,about 83.1 km/h 
C) about 67.5 km/h,about 86.5 km/h 
D) about 23.1 km/h,about 130.9 km/h 
E) about 50.1 km/h,about 103.9 km/h 
A) about 60.2 km/h,about 93.7 km/h 
B) about 70.2 km/h,about 83.1 km/h 
C) about 67.5 km/h,about 86.5 km/h 
D) about 23.1 km/h,about 130.9 km/h 
E) about 50.1 km/h,about 103.9 km/h

Exam 5: The Standard Deviation As a Ruler and the Normal Model

μ = 15.2,15.87% above 16.1;σ = ?

The average weight of a newborn infant is 2.7 kg.An infant that ways 3.15 kg has a z-score of 1.Find the standard deviation.

A town's average snowfall is 40 cm per year with a standard deviation of 5 cm.According to the Normal model,what percent of snowfall is less than 3 standard deviations from the mean?

A bank's loan officer rates applicants for credit.The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50.If an applicant is randomly selected,what percentage can be expected to be between 200 and 275?

Here are the weekly winnings for several local poker players: $100,$50,$125,$75,$80,$60,$110,$150,$300,$700,$115,$75,$1000,$5000.Which is a better summary of the scores,the mean or the median? Explain.

the lowest 40%

The test scores from a recent Mathematics test are as follows: 95.5,65.9,93.2,88.6,56.8,50,86.4,54.5,40.9,77.3,79.5,65.9,70.5,77.3,81.8,50,79.5,and 68.2.The mean score was 71.2 with a standard deviation of 15.5.If the Normal model is appropriate,what percent of the scores will be greater than 86.7?

Here are some statistics for the annual Wildcat golf tournament: lowest score = 58,mean score = 97,median = 105,range = 92,IQR = 105,Q1 = 39,standard deviation = 16.Between what two values are the middle 50% of the scores found?

The average number of babies born in a certain town each year is 218 with a standard deviation of 26.How many standard deviations from the mean is a year with 387 babies born?

Based on the Normal model for snowfall in a certain town N(57,8),how many cm of snow would represent the 25th percentile?

Assuming a Normal model applies,a town's average annual snowfall (in cm)is modeled by N(42,8).Draw and label the Normal model.Then find the interval for the middle 95% of snowfall.

the middle 96%

Here are some summary statistics for the size of forest fires last year: smallest fire = 74 acres,mean = 451 acres,median = 451 acres,range = 7,926 acres,IQR = 387,Q1 = 180,standard deviation = 61 acres.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

For a recent English exam,use the Normal model N(73,9.2)to find the score that represents the 60th percentile.

The scores for a recent English exam can be represented by the Normal model N(67,6.3).What score would you expect to be unusually low for this exam?

The annual snowfall in a town (in cm)can be represented by the Normal model N(45,7.1).What amount of snowfall would you expect to be unusually high for this town?

Based on the Normal model for snowfall in a certain town N(57,8),how many cm of snow would represent the 85th percentile?

Based on the Normal model for car speeds (in km/h)on a road N(77,9.1),what are the cutoff values for the middle 70% of the speeds?

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