Question

For women aged 18 to 24, systolic blood pressure (in mm Hg) is normally distributed with a mean of 114.8 and a standard deviation of 13.1 (based on data from the National Health Survey). Hypertension is commonly defined as a systolic blood pressure above 140. Let X represent the systolic blood pressure of a randomly selected woman between the ages of 18 and 24. a. Find the probability the mean systolic blood pressure of four randomly selected women would fall in the hypertension range (above 140). b. 1% of the mean systolic blood pressures for all possible samples of four randomly selected women between 18 and 24 years are less than what value? c. If a physician is given a report stating that four women have a mean systolic blood pressure below 140, can she conclude that none of the women have hypertension? Explain.

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	114.8
std deviation   =σ=	13.1000
sample size       =n=	4
std error=σx̅=σ/√n=	6.5500

probability the mean systolic blood pressure of four randomly selected women would fall in the hypertension range:

probability =

P(X>140)

=

P(Z>3.85)=

1-P(Z<3.85)=

1-0.9999=

0.0001

b)

for 1st percentile critical value of z=		-2.33
therefore corresponding value=mean+z*std deviation=			99.54

c) No as some women might not have hypertension and therefore their scores are keeping   mean systolic blood pressure below threshold.