The actual mean and standard deviation of this data set are 34.1 mph and 15.3 mph respectivelyWhat RANGE of speeds would 99.7% of animals fall into ? Explain how you found your answer

Answer:

Step-by-step explanation:

Given that the actual mean and standard deviation of the data set are 34.1 mph and 15.3 mph, respectively, we can use the empirical rule (also known as the 68-95-99.7 rule) to determine the range of speeds that 99.7% of animals would fall into.

According to the empirical rule, for a normal distribution, approximately:

*68% of the data falls within one standard deviation of the mean

*95% of the data falls within two standard deviations of the mean

*99.7% of the data falls within three standard deviations of the mean

Therefore, we can determine the range of speeds that 99.7% of animals would fall into by adding and subtracting three standard deviations from the mean.

To calculate this range, we can use the formula:

Range = Mean ± (3 x Standard Deviation)

Plugging in the given values, we get:

Range = 34.1 mph ± (3 x 15.3 mph)

Range = 34.1 mph ± 45.9 mph

Therefore, the range of speeds that 99.7% of animals would fall into is from 34.1 mph - 45.9 mph to 34.1 mph + 45.9 mph, or approximately 0 mph to 80 mph.