For males in a certain town, the systolic blood pressure is normally distributed with a mean of 105 and a standard deviation of 10. Using the empirical rule, determine the interval of systolic blood pressures that represent the middle 99.7% of males.
Question
For males in a certain town, the systolic blood pressure is normally distributed with a mean of 105 and a standard deviation of 10. Using the empirical rule, determine the interval of systolic blood pressures that represent the middle 99.7% of males.
Solution
The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:
- About 68% of the data falls within one standard deviation of the mean.
- About 95% falls within two standard deviations.
- About 99.7% falls within three standard deviations.
In this case, we are looking for the interval that represents the middle 99.7% of males' systolic blood pressures. This corresponds to three standard deviations from the mean.
Step 1: Calculate the value of three standard deviations. Since one standard deviation is 10, three standard deviations would be 3 * 10 = 30.
Step 2: Subtract this value from the mean to find the lower end of the interval. 105 - 30 = 75.
Step 3: Add this value to the mean to find the upper end of the interval. 105 + 30 = 135.
So, the middle 99.7% of systolic blood pressures for males in this town falls within the interval 75 to 135.
Similar Questions
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