Question

The question is on the picture ,I only need help for letter b) 149 cm and 191 cm

Answer 1

The empirical rule is a statistical rule (also called the three-sigma rule or the 68-95-99.7 rule) that states that, for normally distributed data, almost all of the data will fall within three standard deviations on either side of the mean.

This rule states that:

68% of data within 1 standard deviation

95% of data within 2 standard deviations

99.7% of data within 3 standard deviations

The question gives that:

`\begin{gathered} mean=170\text{ cm} \\ sd=7\text{ cm} \end{gathered}`

The question asks to get the percentage of values between 149 cm and 191 cm. If the empirical rule holds, it means that:

`\begin{gathered} 170-7n=149 \\ and \\ 170+7n=191 \end{gathered}`

We can solve for n using any of the equations:

`\begin{gathered} 7n=191-170 \\ 7n=21 \\ n=(21)/(7) \\ n=3 \\ or \\ 7n=170-149=21 \\ n=3 \end{gathered}`

This means that the values lie between 3 standard deviations of the mean.

Therefore, by the Empirical Rule, 99.7% of the men are between 156 cm and 184 cm.