Question

the table below shows the frequency distribution of the rainfall on 52 consecutive tuesdays in a certain city. use the frequency distribution to construct a histogram. do the data appear to have a distribution that is approximately normal?

class	frequency
0.20 – 0.39	11
0.40 – 0.59	6
0.60 – 0.79	3
0.80 – 0.99	4
1.00 – 1.19	4
1.20 – 1.39	1

choose the correct histogram below.

○ a. histogram with 0.0–0.2 bar ~23, 0.2–0.4 ~11, etc.
○ b. histogram with more even bars
○ c. histogram with right skew

Explanation:

Step1: Analyze the frequency distribution

The classes are \(0 - 0.19\) (frequency 23), \(0.20 - 0.39\) (11), \(0.40 - 0.59\) (6), \(0.60 - 0.79\) (3), \(0.80 - 0.99\) (4), \(1.00 - 1.19\) (4), \(1.20 - 1.39\) (1). The frequencies start high, decrease, then slightly increase and decrease again. A normal distribution should be symmetric (bell - shaped), with frequencies increasing to a peak then decreasing. But here, the left side (lower rainfall) has much higher frequencies, and the right side doesn't mirror the left. However, to choose the correct histogram, we match the frequencies to the bar heights. The first class (\(0 - 0.19\)) has the highest frequency (23), then \(0.20 - 0.39\) (11), then \(0.40 - 0.59\) (6), etc. Looking at the options, Option A has a tall bar for the first class, then a shorter one, then even shorter, and the right - side bars are very short, which matches the frequency distribution. Option B has more symmetric right - side bars which don't match the low frequencies on the right (e.g., \(1.20 - 1.39\) has frequency 1, but in B the last bar is not that short). Option C has the tallest bar on the right, which is opposite of our frequency distribution.

Step2: Determine the correct histogram

By comparing the frequency of each class to the bar heights in the options, we see that Option A's bar heights correspond to the given frequencies (tallest for \(0 - 0.19\), then decreasing, with very short bars for the higher - rainfall classes).

Answer:

A. (with the histogram having a tall bar at \(0 - 0.19\), then shorter bars for subsequent classes and very short bars for the highest - rainfall classes)