[0.44/1.1 Points] DETAILS PREVIOUS ANSWERS ILLOWSKYINTROSTAT1 6.1.064.HW. MY NOTES The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean $\mu=130$ and standard deviation $\sigma=12$. (a) Calculate the $z$-scores for the male systolic blood pressures 125 and 135 millimeters. (Round your answers to two decimal places.) \[ \begin{array}{rl} 125 \mathrm{~mm} & z=-0.42 \\ 135 \mathrm{~mm} & z=0.42 \end{array} \] (b) If a male friend of yours said he thought his systolic blood pressure was 2.5 standard deviations below the mean, but that he believed his blood pressure was between 125 and 135 millimeters, what would you say to him? (Enter your numerical answer to the nearest whole number.) $\mathrm{He}$ is 0 because 2.5 standard deviations below the mean would give him a blood pressure reading of millimeters, which is C the range of 125 to 135 millimeters. Submit Answer
Solution
Step 1 ：The problem provides us with the mean (\(\mu\)) and standard deviation (\(\sigma\)) of the systolic blood pressure of males, which are 130 and 12 respectively.
Step 2 ：We are asked to calculate the z-scores for the male systolic blood pressures 125 and 135 millimeters. The z-score is a measure of how many standard deviations an element is from the mean.
Step 3 ：The formula to calculate the z-score is: \[z = \frac{x - \mu}{\sigma}\] where: \(x\) is the value from the dataset (in this case, the blood pressure), \(\mu\) is the mean of the dataset, and \(\sigma\) is the standard deviation of the dataset.
Step 4 ：Substituting the given values into the formula, we get: \[z_{125} = \frac{125 - 130}{12} = -0.42\] and \[z_{135} = \frac{135 - 130}{12} = 0.42\]
Step 5 ：\(\boxed{\begin{array}{rl} 125 \mathrm{~mm} & z=-0.42 \\ 135 \mathrm{~mm} & z=0.42 \end{array}}\)
