Question

Kyle’s doctor told him that the z-score for his systolic blood pressure is $1.75$. Which of the following is the best interpretation of this standardized score? The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean $\mu =125$and standard deviation $\sigma =14$. If X = a systolic blood pressure score then $X~N(125,14)$.

a. Which answer(s) is/are correct?

1. Kyle’s systolic blood pressure is $175$.
2. Kyle’s systolic blood pressure is $1.75$times the average blood pressure of men his age.
3. Kyle’s systolic blood pressure is $1.75$above the average systolic blood pressure of men his age. i
4. Kyles’s systolic blood pressure is$1.75$ standard deviations above the average systolic blood pressure for men.

b. Calculate Kyle’s blood pressure.

Short answer

1. The correct answer is option ivwhich is Kyles’s systolic blood pressure is$1.75$standard deviations above the average systolic blood pressure for men.
2. The blood pressure is $149.5$.

Step-by-step solution

Given information (Part a)

Given in the question that

Mean$=125$

Standard deviation$=14$

$X~N(125,14)$

$X=$systolic blood pressure

Solution (part a)

Here the z- score means the measurement of standard deviation that the raw score is above or below the mean value.

Therefore the z-score $1.75$is positive. which shows the Kyle's blood pressure$1.75$standard deviation is above the mean systolic blood pressure of means

Given information (Part b)

Given in the question that,

Mean$=125$

Standard deviation$=14$

$X~N(125,14)$

$X=$systolic blood pressure

Solution (Part b)

Here we need to calculate the blood pressure that corresponds to the given z-score $1.75$,

$z=\frac{x-\mu }{\sigma }$

$1.75=\frac{x-125}{14}$

$x=(1.75\times 14)+125$

$=149.5$