Question

The National Health Statistics Reports dated Oct. 22, 2008, stated that for a sample size of 277 18-year-old American males, the sample mean waist circumference was 86.3 cm. A somewhat complicated method was used to estimate various population percentiles, resulting in the following values.5th 10th 25th 50th 75th 90th 95th69.6 70.9 75.2 81.3 95.4 107.1 116.4(a)Is it plausible that the waist size distribution is at least approximately normal? Explain your reasoning.

Answer 1

Answer:

It isn't plausible enough to at least say that the distribution is approximately normal because the percentiles given, when plotted on a number line aren't in any way symmetric about the mean as is required for a normal distribution.

Step-by-step explanation:

To investigate whether these values given for the distribution are plausible enough to at least say that the distribution is approximately normal, we will plot the given percentiles on a number line and indicate the median and mean too on that number line.

The spread of the other percentiles about the mean especially and to an extent, the median will show if the distribution is symmetric/ almost symmetric about the mean and the median.

The plot of these percentiles and the mean is presented in the attached image to this answer. The percentiles are indicated with deep dots and the mean is shown with a light square.

The plot shows that the distribution isn't symmetric about the mean and the median. The distribution appears to be skewed to the right.

Hence, it isn't plausible enough to at least say that the distribution is approximately normal because the percentiles given, when plotted on a number line aren't in any way symmetric about the mean as is required for a normal distribution.

Hope this Helps!!!

Answer 2

It isn't plausible that the waist size distribution is at least approximately normal.

What is the distribution of the mean?

The distribution of the mean is determined by taking random samples from data and calculating the mean individually.

The given data

5th 10th 25th 50th 75th 90th 95th

69.6 70.9 75.2 81.3 95.4 107.1 116.4

To determine whether these values given for the distribution are plausible enough for the distribution to be approximately normal, we will plot the given percentiles on a number line and indicate the median and mean.

The plot of these percentiles and the mean shows percentiles that are indicated with deep dots and the mean is shown with a light square.

The plot shows that the distribution isn't symmetric between the mean and the median. The distribution appears to be skewed to the right.

Hence, It isn't plausible that the waist size distribution is at least approximately normal.

Learn more about mean;

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