1 answer

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 171...

Question:

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 171 cm and a standard deviation of 5 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values? a. 161 cm and 181 cm b. 166 cm and 176 cm


Answers

According to the empirical rule, 68%, 95% and 99.7% of data lies within 1, 2 and 3 standard deviations of mean respectively.

a) 171 - 2x5 = 161

171 + 2x5 = 181

So, 161 and 181 cm are the intervals that are 2 standard deviations from mean.

Approximate percentage of values between 161 cm and 181 cm = 95%

b) 171 - 1x5 = 166

171 + 5 = 176

166 and 176 is 1 standard deviation from mean

Approximate percentage of values between 166 cm and 176 cm = 68%

.

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