Question

the table below shows the frequency distribution of the weights (in grams) of pre - 1964 quarters.
weight (g) frequency
6.000 - 6.049 2
6.050 - 6.099 3
6.100 - 6.149 6
6.150 - 6.199 10
6.200 - 6.249 12
6.250 - 6.299 6
6.300 - 6.349 4
6.350 - 6.399 1
use the frequency distribution to construct a histogram. does the histogram appear to depict data that have a normal distribution? why or why not?
choose the correct histogram below.

Explanation:

Step1: Recall normal - distribution characteristics

A normal distribution has a bell - shaped histogram, symmetric about the mean.

Step2: Analyze the given frequency distribution

We look at the frequencies for each weight interval. The frequencies increase from 2 to 12 and then decrease back to 1.

Step3: Check the histograms

We need to find the histogram that represents these frequencies correctly and also check its shape for normality.

• The first histogram has frequencies that match the given distribution well. The frequencies increase to a peak and then decrease. It also has a somewhat symmetric shape around the peak.
• The second histogram has higher frequencies overall and does not match the given distribution.
• The third histogram has incorrect frequencies for some intervals.

Since the first histogram has frequencies that match the given distribution and has a shape that is approximately symmetric (bell - shaped), it appears to depict data that have a normal distribution.

Answer:

The first histogram appears to depict data that have a normal distribution because the frequencies increase to a peak and then decrease in a somewhat symmetric fashion, which is characteristic of a normal distribution.