Question 1

The average score on a mathematics test was 64%.A student who scored 80% had a z-score of 2.Find the standard deviation.

Accepted Answer

A) 16% 
B) 8% 
C) 3% 
D) 20% 
E) 1% 
A) 16% 
B) 8% 
C) 3% 
D) 20% 
E) 1%

Question 2

The speed vehicles travelled on a local road was recorded for one month.The speeds ranged from 46 km/h to 61 km/h with a mean speed of 56 km/h and a standard deviation of 8 km/h.The quartiles and median speeds were 49 km/h,58 km/h,and 53 km/h.Suppose during the month,one driver was clocked at 25 km/h.Which of the summary statistics might not change if that data value was added to the distribution?

Accepted Answer

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

Question 3

A family of four averages 85 loads of laundry per month.One such family does 62 loads per month and has a z-score of -2.3.Find the standard deviation.

Accepted Answer

A) 20 loads 
B) 10 loads 
C) 1 load 
D) 2 loads 
E) 3 loads 
A) 20 loads 
B) 10 loads 
C) 1 load 
D) 2 loads 
E) 3 loads

Question 4

The mean weights for medium navel oranges is 274 grams.Suppose that the standard deviation for the oranges is 92 grams.Which would be more likely,an orange weighing 392 grams or an orange weighing 137 grams? Explain.

Accepted Answer

A) A 137 gram orange is more likely (z = 1.49)compared with an orange weighing 392 grams (z = 4.24). 
B) A 137 gram orange is more likely (z = -1.49)compared with an orange weighing 392 grams (z = 1.28). 
C) A 137 gram orange is more likely (z = 1.28)compared with an orange weighing 392 grams (z = -1.49). 
D) A 392 gram orange is more likely (z = -1.49)compared with an orange weighing 137 grams (z = 1.28). 
E) A 392 gram orange is more likely (z = 1.28)compared with an orange weighing 137 grams (z = -1.49). 
A) A 137 gram orange is more likely (z = 1.49)compared with an orange weighing 392 grams (z = 4.24). 
B) A 137 gram orange is more likely (z = -1.49)compared with an orange weighing 392 grams (z = 1.28). 
C) A 137 gram orange is more likely (z = 1.28)compared with an orange weighing 392 grams (z = -1.49). 
D) A 392 gram orange is more likely (z = -1.49)compared with an orange weighing 137 grams (z = 1.28). 
E) A 392 gram orange is more likely (z = 1.28)compared with an orange weighing 137 grams (z = -1.49).

Question 5

Here are some scores from a recent Mathematics exam: 95.5,65.9,93.2,80.6,56.8,50,86.4,54.5,40.9,77.3,79.5,10,65.9,70.5,15,77.3,81.8,12,50,79.5,60.2.Which is a better summary of the scores,the mean or the median? Explain.

Accepted Answer

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

Question 6

The weights of children age two average 25 pounds with a standard deviation of 4 pounds.How many standard deviations from the mean is a weight of 15 pounds?

Accepted Answer

A) 2.50 standard deviations below the mean 
B) 1.40 standard deviations above the mean 
C) 1.40 standard deviations below the mean 
D) 1.67 standard deviations above the mean 
E) 2.50 standard deviations above the mean 
A) 2.50 standard deviations below the mean 
B) 1.40 standard deviations above the mean 
C) 1.40 standard deviations below the mean 
D) 1.67 standard deviations above the mean 
E) 2.50 standard deviations above the mean

Question 7

After increased patrol,33% of vehicles on a road travel below 45 km/h with a standard deviation of 5.1 km/h.Assuming a Normal model is appropriate,find the mean speed.

Accepted Answer

A) 1.68 km/h 
B) 47.24 km/h 
C) -42.76 km/h 
D) 50.1 km/h 
E) 14..85 km/h 
A) 1.68 km/h 
B) 47.24 km/h 
C) -42.76 km/h 
D) 50.1 km/h 
E) 14..85 km/h

Question 8

σ = 20,48% above 150;μ = ?

Accepted Answer

A) 72 
B) 149 
C) 14.9 
D) 0.48 
E) 0.05 
A) 72 
B) 149 
C) 14.9 
D) 0.48 
E) 0.05

Question 9

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 20% of the speeds?

Accepted Answer

A) about 84.7 km/h,about 69.3 km/h 
B) about 86.1 km/h,about 67.9 km/h 
C) about 61.6 km/h,about 92.4 km/h 
D) about 95.2 km/h,about 58.8 km/h 
E) about 74.7 km/h,about 79.3 km/h 
A) about 84.7 km/h,about 69.3 km/h 
B) about 86.1 km/h,about 67.9 km/h 
C) about 61.6 km/h,about 92.4 km/h 
D) about 95.2 km/h,about 58.8 km/h 
E) about 74.7 km/h,about 79.3 km/h

Question 10

Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest time = 131 minutes,mean = 77 minutes,median = 77 minutes,range = 101 minutes,IQR = 58,Q1 = 31,standard deviation = 15 minutes.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

Accepted Answer

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

Question 11

The average amount of snowfall in a certain town is 54 cm per year.Last year's snowfall was 67.5 cm which corresponded to a z-score of 1.5.Find the standard deviation.

Accepted Answer

A) 5 cm 
B) 30 cm 
C) 9 cm 
D) 20 cm 
E) 1 cm 
A) 5 cm 
B) 30 cm 
C) 9 cm 
D) 20 cm 
E) 1 cm

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

The average score on a mathematics test was 64%.A student who scored 80% had a z-score of 2.Find the standard deviation.

A family of four averages 85 loads of laundry per month.One such family does 62 loads per month and has a z-score of -2.3.Find the standard deviation.

The mean weights for medium navel oranges is 274 grams.Suppose that the standard deviation for the oranges is 92 grams.Which would be more likely,an orange weighing 392 grams or an orange weighing 137 grams? Explain.

Here are some scores from a recent Mathematics exam: 95.5,65.9,93.2,80.6,56.8,50,86.4,54.5,40.9,77.3,79.5,10,65.9,70.5,15,77.3,81.8,12,50,79.5,60.2.Which is a better summary of the scores,the mean or the median? Explain.

The weights of children age two average 25 pounds with a standard deviation of 4 pounds.How many standard deviations from the mean is a weight of 15 pounds?

After increased patrol,33% of vehicles on a road travel below 45 km/h with a standard deviation of 5.1 km/h.Assuming a Normal model is appropriate,find the mean speed.

σ = 20,48% above 150;μ = ?

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 20% of the speeds?

The average amount of snowfall in a certain town is 54 cm per year.Last year's snowfall was 67.5 cm which corresponded to a z-score of 1.5.Find the standard deviation.

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