Question

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Assume that blood pressure is normally distributed.

1. State the random variable.
2. Find the probability that a person in China has blood pressure of 135 mmHg or more.
3. Find the probability that a person in China has blood pressure of 141 mmHg or less.
4. Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
5. Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
6. What blood pressure do 90% of all people in China have less than?

Answer 1

Solution :

a) Let X be a random variable which represents the blood pressure for people in China.

X ~ N(128, 23²)

μ = 128 mmHg and σ = 23 mmHg

b) We have to find P(X ≥ 135 mmHg).

We know that, if X ~ N(μ, σ²) then,

Using "pnorm" function of R we get, P(Z ≥ 0.3043) = 0.3804

Hence, the probability that a person in China has blood pressure of 135 mmHg or more is 0.3804.

c) We have to find P(X ≤ 141 mmHg).

We know that, if X ~ N(μ, σ²) then,

Using "pnorm" function of R we get, P(Z ≤ 0.5652) = 0.7140

Hence, the probability that a person in China has blood pressure of 141 mmHg or less is 0.7140.

d) We have to find P(120 < X < 125).

P(120 < X < 125) = P(X < 125) - P(X ≤ 120)

We know that, if X ~ N(μ, σ²) then,

Using "pnorm" function of R we get,

P(Z < -0.1304) = 0.4481 and P(Z ≤ -0.3478) = 0.3640

Hence, the probability that a person in China has blood pressure between 120 and 125 mmHg is 0.0841.