Question

The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean u = 135 and standard deviation o = 16. (a) Calculate the z-scores for the male systolic blood pressures 125 and 145 millimeters. (Round your answers to two decimal places.) 125 mm z = -0.63 145 mm z = 0.63 (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 145 millimeters, what would you say to him? (Enter your numerical answer to the nearest whole number.) He is incorrect because 2.5 standard deviations below the mean would give him a blood pressure reading of 90 * millimeters, which is below the range of 125 to 145 millimeters. Additional Materials eBook

Answer 1

The z-scores for systolic blood pressures of 100 mmHg and 150 mmHg are -1.79 and 1.79, respectively. A friend claiming that his blood pressure was 2.5 standard deviations below the mean while being between 100 and 150 mmHg is incorrect, as it would actually be 90 mmHg.

Step-by-step explanation:

The systolic blood pressure of males is normally distributed with a mean (μ) of 125 mmHg and a standard deviation (σ) of 14 mmHg.

Part a: Calculating z-scores

To calculate the z-score for a systolic blood pressure reading:

z = (X - μ) / σ

• For 100 mmHg: z = (100 - 125) / 14 = -1.79
• For 150 mmHg: z = (150 - 125) / 14 = 1.79

Part b: Evaluating a Friend's Claim

If a friend claims that his blood pressure is 2.5 standard deviations below the mean, the actual blood pressure reading would be:

Blood pressure = μ + (z × σ)

Blood pressure = 125 + (-2.5 × 14) = 90 mmHg

Therefore, the claim that his systolic blood pressure is between 100 and 150 mmHg while also being 2.5 standard deviations below the mean is incorrect.