Question

Problem 3. According to a recent study the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg.  Assume that blood pressure is normally distributed.

(b)Find the probability that a person in China has blood pressure of140 mmHg or more.

(c)Find the probability that a person in China has blood pressure of 135 mmHg or less.

Continuing with this problem, suppose now a sample of 15 people are chosen from the above normal distribution and we are interested in the mean blood pressure of such a sample.

(h)Find the probability that the sample mean blood pressure of 15 people in China is 140 mmHg or more.

(i)Would it be unusual to find a sample mean blood pressure of 15 people in China of 140 mmHg or more?  Why or why not?

Answer 1

b. Here we need to find $P(x\geq 140)$

As distribution is normal we can convert x to z

$P(x\geq 140)=P(z>\frac{140-128}{23})=P(z>0.52)=0.3015$

$1586465348368_blob.png$

c. $P(x\leq 135)=P(z<\frac{135-128}{23})=P(z<0.30)=0.6179$

$1586465404288_blob.png$

h. Here we need to find $P(\overline{x}\geq 140)$

As population is normal, as per central limit theorem sample mean is also normal so we can convert sample mean to z

$P(\overline{x}\geq 140)=P(z>\frac{140-128}{\frac{23}{\sqrt{15}}})=P(z>2.02)=0.0217$

$1586465567304_blob.png$

i. As probability is less than 0.05, it is unusual.