Question

The data represents the daily rainfall​ (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of 0.20. Does the frequency distribution appear to be roughly a normal​ distribution?

Answer 1

The question is incomplete! Complete question along with step by step explanation is provided below!

Question:

The data represents the daily rainfall​ (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of 0.20. Does the frequency distribution appear to be roughly a normal​ distribution?

0.48 0 0.09 0.17 0 0 0.21 0 0.59 0.13 0 0 0.01 0 0 0.23 0 0 0.01 0 0 1.24 0.24 0 0.05 0.65 0 0 0.28 0

Answer:

No, the given frequency distribution does not appear to be a normal​ distribution.

Step by Step Explanation:

Monthly rainfall data is given each value represents 1 day and total data points are 30.

0.48 0 0.09 0.17 0 0 0.21 0 0.59 0.13 0 0 0.01 0 0 0.23 0 0 0.01 0 0 1.24 0.24 0 0.05 0.65 0 0 0.28 0

First we will construct a frequency distribution stating at 0.00 with 0.20 width and ending at 1.40.

Range            |    Frequency

0.00 - 0.20    |    22

0.20 - 0.40    |    4

0.40 - 0.60    |    2

0.60 - 0.80    |    1

0.80 - 1.00    |    0

1.00 - 1.20     |    0

1.20 - 1.40     |    1

Mean = (0.10*22+0.30*4+0.50*2+0.70*1+1.3*1)/30 = 0.21

where midpoint is calculate using (lower limit + upper limit)/2

In a normal distribution, frequencies start off low then increase gradually then decrease gradually and finally end off low.

But in this distribution, as you can see frequencies doesn't start off low but rather the opposite is true. The distribution is very much skewed at the beginning since mean is 0.21 and also the distribution is not symmetric.

Conclusion:

Hence we can conclude that the given frequency distribution does not appear to be a normal​ distribution.