Part B - Using the 68−95−99.7 Rule

A rule of thumb for normal distributions is the following:

- Approximately 68% of observations are within 1 standard deviation of the mean.
- Approximately 95% of observations are within 2 standard deviations of the mean.
- Approximately 99.7% of observations are within 3 standard deviations of the mean.

Use the 68-95-99.7 rule to approximate the following percentages:

3. The percentage of days less than 77.4 degrees.

4. The percentage of days greater than 78.6 degrees.

Using the 68-95-99.7 rule for normal distributions, approximately 68% of days fall within 1 standard deviation of the mean, estimating the percentages for days less than 77.4 degrees and greater than 78.6 degrees to be around 68% each.

To approximate the percentages using the 68-95-99.7 rule for normal distributions:

The percentage of days less than 77.4 degrees:

Since the mean is not given, let's assume the mean is 78 degrees for simplicity.

1 standard deviation would be approximately 1 degree.

So, within 1 standard deviation below the mean (77 degrees), around 68% of the data falls.

Therefore, the percentage of days less than 77.4 degrees can be approximated as around 68%.

The percentage of days greater than 78.6 degrees:

Similarly, within 1 standard deviation above the mean (79 degrees), around 68% of the data falls.

Since the total percentage is 100%, the percentage of days greater than 78.6 degrees would also be around 68%.

Learn more about percentages:-

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