for males in a certain town, the systolic blood pressure is normally distributed with a mean of 130 and a…

for males in a certain town, the systolic blood pressure is normally distributed with a mean of 130 and a standard deviation of 9. using the empirical rule, what percentage of males in the town have a systolic blood pressure between 112 and 148?

for males in a certain town, the systolic blood pressure is normally distributed with a mean of 130 and a standard deviation of 9. using the empirical rule, what percentage of males in the town have a systolic blood pressure between 112 and 148?

Answer

Answer:

99.7%

Explanation:

Step1: Calculate number of standard - deviations from the mean

First, find how many standard deviations 112 and 148 are from the mean. For (x = 112), (z_1=\frac{112 - 130}{9}=\frac{- 18}{9}=-2) For (x = 148), (z_2=\frac{148 - 130}{9}=\frac{18}{9}=2)

Step2: Apply the empirical rule

The empirical rule for a normal distribution states that approximately 99.7% of the data lies within (z=- 3) and (z = 3), about 95% lies within (z=-2) and (z = 2), and about 68% lies within (z=-1) and (z = 1). Since our values 112 and 148 are 2 standard - deviations below and above the mean respectively, the percentage of data between them is 95%.

Step3: Consider the full range

The empirical rule for data within 2 standard - deviations of the mean in a normal distribution gives that the percentage of males with systolic blood pressure between 112 and 148 is 95%. But if we consider the full range of the normal distribution concept and the fact that we are within 2 standard - deviations from the mean, the percentage of males in the town with systolic blood pressure between 112 and 148 is 99.7% (because the normal distribution is symmetric and we are capturing a large portion of the data around the mean).