Questions: In the Northern Hemisphere, dolphins swim predominantly in a counterclockwise direction while sleeping. A group of researchers wanted to know whether the opposite was true for dolphins in the Southern Hemisphere (Stafne and Manger 2004). They watched eight sleeping dolphins and recorded the percentage of time that the dolphins swam clockwise. Assume that this is a random sample and that this variable has a normal distribution in the population. These data are as follows: 77.7,84.8,79.4,84.0,99.6,93.6,89.4,97.2 Click to download the data in your preferred format. CSV Excel JMP Mac-Text Minitab PC-Text R SPSS TI CrunchIt! What is the mean percentage of clockwise swimming for Southern Hemisphere dolphins? Round your answer with precision to one decimal place. mean percentage: %

In the Northern Hemisphere, dolphins swim predominantly in a counterclockwise direction while sleeping. A group of researchers wanted to know whether the opposite was true for dolphins in the Southern Hemisphere (Stafne and Manger 2004). They watched eight sleeping dolphins and recorded the percentage of time that the dolphins swam clockwise. Assume that this is a random sample and that this variable has a normal distribution in the population. These data are as follows: 77.7,84.8,79.4,84.0,99.6,93.6,89.4,97.2 Click to download the data in your preferred format. CSV Excel JMP Mac-Text Minitab PC-Text R SPSS TI CrunchIt! What is the mean percentage of clockwise swimming for Southern Hemisphere dolphins? Round your answer with precision to one decimal place. mean percentage: %
Transcript text: In the Northern Hemisphere, dolphins swim predominantly in a counterclockwise direction while sleeping. A group of researchers wanted to know whether the opposite was true for dolphins in the Southern Hemisphere (Stafne and Manger 2004). They watched eight sleeping dolphins and recorded the percentage of time that the dolphins swam clockwise. Assume that this is a random sample and that this variable has a normal distribution in the population. These data are as follows: \[ 77.7,84.8,79.4,84.0,99.6,93.6,89.4,97.2 \] Click to download the data in your preferred format. CSV Excel JMP Mac-Text Minitab PC-Text R SPSS TI CrunchIt! 10 What is the mean percentage of clockwise swimming for Southern Hemisphere dolphins? Round your answer with precision to one decimal place. mean percentage: $\square$ \%
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Solution

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Solution Steps

Step 1: Calculate the Sum of the Data

To find the mean percentage of clockwise swimming for Southern Hemisphere dolphins, we first calculate the sum of the recorded percentages:

\[ \sum_{i=1}^N x_i = 77.7 + 84.8 + 79.4 + 84.0 + 99.6 + 93.6 + 89.4 + 97.2 = 705.7 \]

Step 2: Determine the Number of Observations

The number of observations \( N \) is given as:

\[ N = 8 \]

Step 3: Calculate the Mean

The mean \( \mu \) is calculated using the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} = \frac{705.7}{8} = 88.2125 \]

Rounding this value to one decimal place gives:

\[ \mu \approx 88.2 \]

Final Answer

The mean percentage of clockwise swimming for Southern Hemisphere dolphins is \\(\boxed{88.2\%}\\).

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