For a set of data with a mound-shaped relative frequency distribution, what can

Question

For a set of data with a mound-shaped relative frequency distribution, what can be said about the percentage of the measurements contained in each of the intervals specified below?

a) x s to x + s

b) x 2s to x + 2s

c) x 3s to x + 3s

a) Determine, if possible, the percentage of measurements within the interval x s to x + s.

A. The number of measurements within this interval is approximately 5/8 of the total number of measurements.

B. The number of measurements within this interval is approximately 0.5 of the total number of measurements.

C. The number of measurements within this interval is approximately 68% of the total number of measurements.

D. No useful information can be determined about the percentage of measurements in this interval.

b) Determine, if possible, the percentage of measurements within the interval x 2s to x + 2s.

A. The number of measurements within this interval is approximately 0.89 of the total number of measurements.

B. The number of measurements within this interval is approximately 95% of the total number of measurements.

C. The number of measurements within this interval is approximately 3/4 of the total number of measurements.Your answer is not correct.

D. No useful information can be determined about the percentage of measurements in this interval.

c) Determine, if possible, the percentage of measurements within the interval x 3s to x + 3s.

A. The number of measurements within this interval is approximately 0.96 of the total number of measurements.

B. The number of measurements within this interval is approximately 8/9 of the total number of measurements.Your answer is not correct.

C. The number of measurements within this interval is approximately 99.7% of the total number of measurements.

D. No useful information can be determined about the percentage of measurements in this interval.

Explanation / Answer

In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively.

Thus.

a) one standard deviation from mean => 68% Option C (The number of measurements within this interval is approximately 68% of the total number of measurements)

b) two standard deviation from mean => 95% Option B (The number of measurements within this interval is approximately 95% of the total number of measurements)

c) three standard deviation from mean => 99.7% Option C (The number of measurements within this interval is approximately 99.7% of the total number of measurements)

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.