Question

Q-7 (7.16). The body mass index (BMI) of a person is defined to be the person's body mass (in kg) divided by the person's height squared (in m). Consider a population of males with a mean BMI of 3.2 kg/m2 and standard deviation of 0.17 kg/m2. We select n = 33 individuals from this population. (a) Let X be the mean BMI for the 33 individuals. Give the expected value and the standard deviation of X. (b) Compute P(X> 3.3)

Answer 1

a)
expected value = 3.2
std. dev. (xbar) = 0.17/sqrt(33) = 0.0296

b)
Here, μ = 3.2, σ = 0.0296 and x = 3.3. We need to compute P(X >= 3.3). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (3.3 - 3.2)/0.0296 = 3.38

Therefore,
P(X >= 3.3) = P(z <= (3.3 - 3.2)/0.0296)
= P(z >= 3.38)
= 1 - 0.9996
= 0.0004