Question

For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. Hypertension is commonly defined as a systolic blood pressure above 140. If 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140.

Answer 1

Answer: 0.0001

Step-by-step explanation:

Given : For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1.

i.e. $\mu=114.8\ \ \ \&\ \ \sigma=13.1$

Sample size =4

Let x be the sample mean systolic blood pressure.

Then the probability that their mean systolic blood pressure is greater than 140 will be

$P(x>140)=1-P(x\leq140)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\leq\dfrac{140-114.8}{\dfrac{13.1}{\sqrt{4}}})\\\\\ =1-P(z\leq3.85)\ \ [\because \ z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9999\ \ \text{[By z-table]}\\\\= 0.0001$

Hence, the required probability = 0.0001