Question

A national survey revealed that the proportion of adults with high blood pressure is 0.3. A sample of 125 U.S. adults is chosen. Find the probability that less than 25% of the people in the sample have high blood pressure. Answer:

Answer 1

Answer:

Given that,

$\rightarrow$ A national survey revealed that the proportion of adults with high blood pressure is 0.3. A sample of 125 U.S. adults is chosen.

Find the probability that less than 25% of the people in the sample have high blood pressure:

For normal distribution Z-score is=

P-P OP

here,

$\hat{p}=0.25$

The population proportion (p)=0.3

The sample size (n)=125

Then,

The standard errof of proportion is,

$\sigma _{p}=\sqrt{\frac{p(1-p)}{n}}$

0.311-0.3) 125

=0.041

$\rightarrow$ The probability that less than 25% of the people in the sample have high blood pressure is,

P(X < 0.25):

$P(X < 0.25)=P(\frac{\hat{p}-p}{\sigma _{p}}<\frac{0.25-0.3}{0.041})$

$=P(Z<\frac{0.25-0.3}{0.041})$

=P(Z<-0.05/0.041)

=P(Z < -1.22)

=0.1112

Therefore, the probability that less than 25% of the people in the sample have high blood pressure is, P(X < 0.25)=0.1112.

**Please comment on any doubt.