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Answer :
Final answer:
Using the Empirical Rule for a bell-shaped distribution, about 95% of the men will have heights between 169 cm and 193 cm, and about 68% between 175 cm and 187 cm.
Explanation:
The heights of men on a baseball team have a bell-shaped distribution with a mean of 181 cm and a standard deviation of 6 cm. Using the Empirical Rule that explains that approximately 68 percent of the data will fall within one standard deviation of the mean, 95 percent will fall within two standard deviations, and 99.7 percent within three standard deviations, we can answer your questions:
- a. 169 cm and 193 cm: These values are one standard deviation away from the mean (181 cm - 12 cm = 169 cm, and 181 cm + 12 cm = 193 cm). Therefore, about 95 percent of the men will have heights in between these values.
- b. 175 cm and 187 cm: These values are within one standard deviation from the mean (181 cm - 6 cm = 175 cm, and 181 cm + 6 cm = 187 cm). Therefore, about 68 percent of the men will have heights between this range.
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Answer:
Approximate 95% of the men between 169 cm and 193 cm and approximate 68% the men between 175 cm and 187 cm
Step-by-step explanation:
[tex]\text{z score} = \dfrac {raw\ score - mean}{standard\ deviation}[/tex]
We have,
mean = 181 cm, standard deviation = 6cm
Now, we have to find the approximate percentage of the men between 169 cm and 193 cm and 175 cm and 187 cm
[tex]z_1a = \dfrac{169 - 181}{6} = \dfrac {-12}6 = -2\\\\z_1b = \dfrac{193- 181}{6} = \dfrac {12}6 = 2\\\\z_2a = \dfrac {175 - 181}6 = \dfrac {-6}6 = -1\\\\z_2b = \dfrac{187 - 181}{6} = \dfrac {6}6 = 1[/tex]
the empirical rule says:
68 percent of data points for a normal distribution will fall within 1 standard deviation, 95 percent within 2 standard deviations, and 99.7 percent within 3 standard deviations.
So,
Approximate 95% of the men between 169 cm and 193 cm and approximate 68% the men between 175 cm and 187 cm.
