Reporting summary measures such as the mean, median, and standard deviation has become very common in modern life. Many companies, government agencies will report these descriptive measures of a variable, but they will rarely provide information on the shape of the distribution of that variable. In previous tutorials, you have learned some basic properties of some distributions that can help you to decide if a specific type of distribution is a good fit for a set of data. According to the National Diet and Nutrition Survey: Adults Aged 19 to 64, British men spend an average of 2.15 hours per day in moderate or high intensity physical activity. The standard deviation of these activity times for this sample was 3.59 hours. Can we infer that these activity times could follow a normal distribution? The following may provide an answer. Suppose that the standard deviation for this sample was 0.70 hours instead of 3.59 hours, which make it numerically possible for the distribution to be normal. Again, considering the variable being measured, explain why the normal distribution is still not a logical choice for this distribution.

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Reporting summary measures such as the mean, median, and standard deviation has become very common in modern life. Many companies, government agencies will report these descriptive measures of a variable, but they will rarely provide information on the shape of the distribution of that variable. In previous tutorials, you have learned some basic properties of some distributions that can help you to decide if a specific type of distribution is a good fit for a set of data.  According to the National Diet and Nutrition Survey: Adults Aged 19 to 64, British men spend an average of 2.15 hours per day in moderate or high intensity physical activity. The standard deviation of these activity times for this sample was 3.59 hours. Can we infer that these activity times could follow a normal distribution? The following may provide an answer.  Suppose that the standard deviation for this sample was 0.70 hours instead of 3.59 hours, which make it numerically possible for the distribution to be normal. Again, considering the variable being measured, explain why the normal distribution is still not a logical choice for this distribution.

sweererlirumeX · Accepted Answer

Step 1  Given information:  μ=2.15  σ=0.70  Step 2  Use the given mean and new standard deviation to determine the interval for below and above standard deviations values.  μ±1⋅σ=2.15±1⋅(0.70)  =(1.45, 2.85)  μ±2⋅σ=2.15±⋅(0.70)  =(0.75, 3.55)  μ±3⋅σ=2.15±3⋅(0.70)  =(0.05, 4.25)  Now the above distribution is numerically possible for the distribution to be normal, because both the three standard deviation below and above the mean values for number of hours spent in moderate or high intensity physical activity are positive.  Step 3  If the above distribution has to follow the normal distribution, then the interval for three standard deviation below and above the mean values should contain 99.7% of the data values. However this would not be practically possible, because many British men spend an average of 7 to 8 hours per day in moderate or high intensity physical activity. Therefore the normal distribution is still not a logical choice for this distribution.

Reporting summary measures such as the mean, median, and standard deviation has

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