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Answer :
a. Approximately 99.7% of the men have heights between 139 cm and 193 cm. b. Approximately 68% of the men have heights between 157 cm and 175 cm.
The empirical rule (also known as the 68-95-99.7 rule) states that for a normal (bell-shaped) distribution:
About 68% of the data falls within one standard deviation of the mean.
About 95% of the data falls within two standard deviations of the mean.
About 99.7% of the data falls within three standard deviations of the mean.
Given:
Mean (μ) = 166 cm, Standard deviation (σ) = 9 cm
a. Heights between 139 cm and 193 cm:
First, determine how many standard deviations away from the mean these values are:
Lower bound = μ−3σ = 166−3(9) = 166−27 = 139cm
Upper bound = μ+3σ = 166+3(9) = 166+27 = 193cm
Since 139 cm and 193 cm are three standard deviations below and above the mean, respectively, the empirical rule tells us that approximately 99.7% of the data falls within this range.
b. Heights between 157 cm and 175 cm:
Next, determine how many standard deviations away from the mean these values are:
Lower bound = μ−σ = 166−9 = 157cm
Upper bound = μ+σ = 166+9 = 175cm
Since 157 cm and 175 cm are one standard deviation below and above the mean, respectively, the empirical rule tells us that approximately 68% of the data falls within this range.
Complete Question:
Heights of men on a baseball team have a bell-shaped distribution with a mean of 166 cm and a standard deviation of 9 cm. Using the empirical rule, what is the approximate percentage of the men between the folowing values? a. 139 cm and 193 cm b. 157 cm and 175 cm
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