Chapter 2 Test Review

Page 137 #T.2.1 (Interpreting Percentiles)

• a

• b

• c

• d

• e

Answer explanation

The percentile tells you the percent of the data set that is at or below a specific piece of data.

Page 138 #T.2.5 (Calculate the standard deviation from a percentile.)

• a

• b

• c

• d

• e

Answer explanation

15% is the area to the right of 60 inches. You need to look in Table A for 0.85, which is the area to the left. Then use the corresponding z-score and the z-score formula to solve for the standard deviation.

Page 138 #T.2.7 (Calculate the standard deviation using the empirical rule)

• a

• b

• c

• d

• e

Answer explanation

Using the 68-95-99.7 rule, if 99.7% of the data lies between 5 ft & 7ft, these numbers are both 3 standard deviations from the mean. The mean is between them at 6ft., so the standard deviation must be 1/3 of a foot (4 inches).

Page 138 #T.2.10 (Comparing Standardized Scores)

• a

• b

• c

• d

• e

Answer explanation

Calculate the z-scores for each student. The student with the higher z-score performed better compared to their peers.

The number of absences during fall semester was recorded for each student in a large elementary school. The distribution of absences is displayed in the following cumulative relative frequency graph. What is the IQR for the distribution of absences?

• 1

• 2

• 3

• 5

• 1

Answer explanation

Q1 is found at the 25th percentile. Q3 is found at the 75th percentile. Subtract those values to find your IQR.

The weights of laboratory cockroaches follow a Normal distribution with mean 80 grams and standard deviation 2 grams. The following figure is the Normal curve for the distribution of weights. About what percent of the cockroaches have weights between 76 and 84 grams?

• 99.7%

• 95%

• 68%

• 47.5%

• 34%

Answer explanation

Use the empirical Rule (68-95-99.7 rule). Since 76 & 84 are both 2 standard deviation from the mean, this rule is easily applied.

For the density curve shown, which of the following statements is true?

• The mean is larger than the median.

• The proportion of outcomes between 0.2 and 0.5 is equal to 0.3.

• The proportion of outcomes greater than 1.5 is equal to 0.25.

• The area under the curve is 2.

Answer explanation

This is a uniform distribution. The area of the curve is length times width.

The cumulative relative frequency graph describes the distribution of weights (in grams) of tomatoes grown in a laboratory experiment. Which of the following weights is closest to the median of the distribution?

• 120 grams

• 140 grams

• 170 grams

• 200 grams

Answer explanation

The median is found at the 50the percentile.

Page 139 #T.2.12 (Percentile, finding percentage, finding the IQR)

Answer explanation

a) 23.9 is 1 standard deviation above the mean. Use the 68-95-99.7 rule to determine the are under the curve.

b) Find z-scores for 20 inches & 26 inches. Then use table A to find the area between those z-scores.

c) Q1 will be found at 25% and Q3 will be found at 75%. Use these values on Table A to come up with the z-scores for those data points.

Page 139 #T.2.13 (Assessing Normality)

Answer explanation

The mean & median are not close to each other.

The distance between the median and the minimum is very different than the distance from the median to the maximum. If the distribution was Normal, these would be much more similar because of the symmetric nature.