Question

#48 according to the “empirical rule”, what percentage of credit loads would you expect to lie outside two (2) standard deviation units from the mean? (a) 50% (b) 32% (c) 25% (d) 5% (e) 0.3% #49 according to the “empirical rule”, what percentage of credit loads would you expect to lie outside three (3) standard deviation units from the mean? (a) 50% (b) 32% (c) 25% (d) 5% (e) 0.3% #50 the first (i.e. lower) quartile is the same as which percentile? (a) 25th (b) 50th (c) 75th (d) 90th (e) 95th #51 the second (i.e. middle) quartile is the same as which percentile? (a) 25th (b) 50th (c) 75th (d) 90th (e) 95th

Explanation:

Step1: Recall empirical - rule for 2 standard deviations

The empirical rule states that about 95% of the data lies within 2 standard deviations of the mean. So the percentage outside 2 standard deviations is \(100 - 95=5\%\).

Step2: Recall empirical - rule for 3 standard deviations

The empirical rule states that about 99.7% of the data lies within 3 standard deviations of the mean. So the percentage outside 3 standard deviations is \(100 - 99.7 = 0.3\%\).

Step3: Recall quartile - percentile relationship for first quartile

The first (lower) quartile \(Q_1\) divides the data such that 25% of the data is below it. So the first quartile is the 25th percentile.

Step4: Recall quartile - percentile relationship for second quartile

The second (middle) quartile \(Q_2\) is the median. It divides the data such that 50% of the data is below it. So the second quartile is the 50th percentile.

Answer:

#48: D. 5%
#49: E. 0.3%
#50: A. 25th
#51: B. 50th