# a. The range of WR scores that would contain about

a. The range of WR scores that would contain about 95% of the scores in the drug dealer sample.
Given info:
The data have mount-shaped, symmetric distribution.
$$\displaystyle{n}={100},\overline{{{x}}}={39},{s}={6}$$.
b. The proportion of scores that lies above 51.
c. The range of WR scores that contain nearly all samples of drug dealer sample.

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dieseisB
a) Calculation:
Empirical rule:
Empirical rule is a rule that can be applied to a data set with mound-shaped, symmetric frequency distributions.
The rule says that approximately 68% measurements will lie between 1 standard deviation of the data, 95% will lie between 2 standard deviations and 99.7% will lie between 3 standard deviations of mean.
The data have mound-shaped, symmetric distribution. Therefore, the empirical rule can be applied. Using empirical rule, 95% of observations lie between 2 standard deviations of mean.
That is, the interval has 95% of observations that would be $$\displaystyle{\left(\overline{{{x}}}\pm{2}{s}\right)}$$
Upper limit of interval:
$$\displaystyle\overline{{{x}}}+{2}\times{s}={39}+{2}\times{6}={51}$$
Lower limit of interval:
$$\displaystyle\overline{{{x}}}-{2}\times{s}={39}-{2}\times{6}={27}$$
Thus, the interval is (27,51).
b) The distribution of data is symmetric. From part a, it is clear that 95% that is 0.95 observations lie between (27 and 51). Therefore, the remaining 0.05 observations will lie outside the interval. Since the distribution is symmetric, the proportion of observations, which lies below 27 and above 51, will be the same.
Thus, half of 0.05 observations will lie above. That is, $$\displaystyle{\frac{{{0.05}}}{{{2}}}}={0.025}$$ observations will lie above 51.
c) Calculation:
Empirical rule:
Empirical rule is a rule that can be applied to a data set with mound-shaped, symmetric frequency distributions.
The rule says that approximately 68% measurements will lie between 1 standard deviation of the data, 95% will lie between 2 standard deviations and 99.7% lie between 3 standard deviations of mean.
The data have mount-shaped, symmetric distribution. Therefore, empirical rule can be applied. Using empirical rule, 99.7% of observations lie between 3 standard deviations of the mean that is almost all observations in the data.
That is, interval has 97.9% of observations that would be $$\displaystyle{\left(\overline{{{x}}}\pm{3}{s}\right)}$$.
Upper limit of interval:
$$\displaystyle\overline{{{x}}}+{3}\times{s}={39}+{3}\times{6}={57}$$
Lower limit of interval:
$$\displaystyle\overline{{{x}}}-{3}\times{s}={39}-{3}\times{6}={21}$$
Thus, the interval is (21,57).