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A biologist measures the stride lengths of a population of emus, the second-tallest birds in the world, and the stride lengths of a population of ostriches, the tallest birds in the world. The biologist found that the stride lengths of both populations were approximately normally distributed.
• The mean stride length of the population of emus is 3 meters with a standard deviation of 0.5 meters.
• The mean stride length of the population of ostriches is 4.5 meters with a standard deviation of 0.75 meters.

o Approximately 34% of the ostriches have stride lengths between 4.5 and 5.25 meters. Describe these values in terms of the mean and standard deviation only. What interval would represent a similar percentage of emus?
o How can this percentage be seen using a graph of the normal curve?

1 Answer

4 votes

Answer:

34 PERCENT

Explanation:

To describe the stride lengths of ostriches in terms of the mean and standard deviation only, we can use the empirical rule (also known as the 68-95-99.7 rule). According to this rule, for a normal distribution:

- Approximately 68% of the data falls within one standard deviation of the mean.

- Approximately 95% of the data falls within two standard deviations of the mean.

- Approximately 99.7% of the data falls within three standard deviations of the mean.

Since the mean stride length of ostriches is 4.5 meters and the standard deviation is 0.75 meters, a stride length between 4.5 and 5.25 meters is within one standard deviation above the mean. Therefore, approximately 34% of the ostriches have stride lengths between 4.5 and 5.25 meters.

To find a similar percentage of emus, we can use the same approach. Since the mean stride length of emus is 3 meters and the standard deviation is 0.5 meters, we need to find the interval that is one standard deviation above the mean. This interval is from 3.5 meters to 2.5 meters, so approximately 34% of the emus have stride lengths between 2.5 and 3.5 meters.

To see this percentage using a graph of the normal curve, we can draw the curve for the distribution of ostrich stride lengths with mean 4.5 meters and standard deviation 0.75 meters. The area under the curve between 4.5 and 5.25 meters represents the percentage of ostriches with stride lengths in that range, which is approximately 34%. Similarly, we can draw the curve for the distribution of emu stride lengths with mean 3 meters and standard deviation 0.5 meters. The area under the curve between 2.5 and 3.5 meters represents the percentage of emus with stride lengths in that range, which is also approximately 34%.

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User Denis Mysenko
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