Question

the frequency - distribution below represents magazine readership frequencies recorded during the course of a 31 - day month. use the frequency - distribution to construct a histogram. do the data appear to have a distribution that is approximately normal?
class\tfrequency
a 39 - 44\t1
b 45 - 50\t1
c 51 - 56\t5
d 57 - 62\t12
e 63 - 68\t8
f 69 - 74\t2
g 75 - 80\t2
choose the correct histogram below.
do the data appear to have a distribution that is approximately normal?
a. no, it is completely skewed.
b. no, it is not at all symmetric.
c. no, it is approximately uniform.
d. yes, it is approximately normal.

Explanation:

Step1: Recall properties of normal - distribution histogram

A normal - distribution histogram is symmetric about the mean, with the frequencies starting low, increasing to a maximum at the middle class(es), and then decreasing symmetrically.

Step2: Analyze the given frequency distribution

The class frequencies are 1, 1, 5, 12, 8, 2, 2. The frequencies increase from the first two classes to the class 51 - 56 (with frequency 12) and then start to decrease. But the decrease is not symmetric. For example, the frequencies on the left - hand side of the peak class (1, 1, 5) do not mirror the frequencies on the right - hand side (8, 2, 2) in a symmetric way.

Answer:

B. No, it is not at all symmetric