R. Reifen et al. studied various nutritional measures of Ethiopian school children and published their findings in the paper "Ethiopian-Born and Native Israeli School Children Have Different Growth Patterns" (Nutrition, Vol. 19, pp. 427-431). The study, conducted in Azezo, North West Ethiopia, found that malnutrition is prevalent in primary and secondary school children because of economic poverty. The weights, in kilograms (kg), of 60 randomly selected male Ethiopian-born school children aged 12-15 years old are presented in increasing order in the following table.

The sample mean and sample standard deviation of these weights are 45.30 kg and 4.16 kg, respectively. A histogram of the weights is shown in Exercise 2.142 on page 81. Modeling your solutions after those in Example 3.17 on pages 119-121, solve the following problems.
a. Is it reasonable to apply the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean?
b. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean.
c. Use the data to obtain the exact percentages of observations that lie within one, two, and three standard deviations to either side of the mean.
d. Compare your answers in parts (b) and (c).

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36.3 37.7 38.0 38.8 38.9 39.0 39.3 40.9 41.1 41.3 41.5 41.8 42.0 42.0 42.1 42.5 42.5 42.8 42.9 43.3 43.4 43.5 44.0 44.4 44.7 44.8 45.2 45.2 45.2 45.4 5.5 45.7 45.9 45.9 46.2 46.3 46.5 46.6 46.8 47.2 47.4 47.5 47.8 47.9 48.1 48.2 48.3 48.4 48.5 48.6 48.9 49.1 49.2 49.5 50.9 51.4 51.8 52.8 53.8 56.6