Question

The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean $\mu =125$and standard deviation $\sigma =14$. Systolic blood pressure for males follows a normal distribution.

a. Calculate the z-scores for the male systolic blood pressures $100$and $150$millimeters.

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 $100$ and $150$ millimeters, what would you say to him?

Short answer

1. The z-score of the systolic blood pressures $100$is $-1.79$and $150$is $1.79$.
2. The given z-score is more than the given range $100$ and $150$ so, the friends believe is wrong.

Step-by-step solution

Given information (Part a)

Given in the question that

Mean$=125$

Standard deviation$=14$

$X~N(125,14)$

Solution (Part a)

Here we need to calculate the z-score for $100$

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

$=\frac{100-125}{14}$

$=-1.79$

Again we need to calculate the z-score of $150$

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

$=\frac{150-125}{14}$

$=1.79$

Given information (Part b)

Given in the question that

Mean $=125$

Standard deviation $=14$

$X~N(125,14)$

Solution (Part b)

Here the z-score has been given as $2.5$and we need to find the blood pressure,

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

$2.5=\frac{x-125}{14}$

$x=2.5\times 14+125$

$=160$