Question

A. The distribution of the height (X) in centimeter (CM) of the 16 teachers of SCNHS was presented below. construct a histogram for the random variable (X).

X | F

138 | 1

139 | 2

140 | 3

141 | 4

142 | 3

143 | 2

144 | 1

B. Use Empircal rule to complete the following table. write on the respective column the range or interval of the scores based on the given parameters.

        |MEAN | STANDARD DEVIATION | 68% | 95% | 99.7% |
      1 | 135 |    28              |     |     |       |
      2 | 87  |    5.5             |     |     |       |
      3 | 213 |    15              |     |     |       |
      4 | 567 |    20              |     |     |       |
      5 | 785 |    29              |     |     |       |
c. Illustrate the distribution in activity b through diagram.

Answer 1

A.

B.

Empircal rule:

68% of the data falls within one standard deviation from the mean: $\mu\pm \sigma$

95% of the data falls within two standard deviations from the mean : $\mu\pm 2\sigma$

99.7% of the data falls within one standard deviation from the mean: $\mu\pm 3\sigma$

1.

68%: $135\pm 28=(107,163)$

95%: $135\pm 56=(79,191)$

99.7%: $135\pm 84=(51,219)$

2.

68%: $87\pm 5.5=(81.5,92.5)$

95%: $87\pm 11=(76,98)$

99.7%: $87\pm 16.5=(70.5,103.5)$

3.

68%: $213\pm 15=(198,228)$

95%: $213\pm 30=(183,243)$

99.7%: $213\pm 45=(168,258)$

4.

68%: $567\pm 20=(547,587)$

95%: $567\pm 40=(527,607)$

99.7%: $567\pm 60=(507,627)$

5.

68%: $785\pm 29=(756,814)$

95%: $785\pm 58=(727,843)$

99.7%: $785\pm 87=(698,872)$