Question

Gina's doctor told her the standardized score (z-score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is 1.50. Which of the following is the best interpretation of this standardized score?
a. Gina's systolic blood pressure is 150.
b. Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.
c. Gina's systolic blood pressure is 1.50 above the average systolic blood pressure of women her age.
d. Gina's systolic blood pressure is 1.50 times the average systolic blood pressure for women her age.
e. Only 1.5% of women Gina's age have a higher systolic blood pressure than she does.

Answer 1

Answer:

Option b) Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.            

Step-by-step explanation:

We are given the following in the question:

The distribution of systolic blood pressure of other women is a bell shaped distribution that is a normal distribution.

z-score = 1.50

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

Let x be the Gina's systolic blood pressure.

Thus, we can write:

$1.50 = \displaystyle\frac{x-\mu}{\sigma}\\\\x = 1.5\sigma + \mu \\\text{where }\sigma \text{ is the standard deviation and }\\\mu \text{ is the mean for the given distribution of blood pressure.}$

Thus, we can write Gina's blood pressure  is 1.50 standard deviations above the average systolic blood pressure of women her age.

Option b) Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.