Question

Suppose systolic blood pressure of 17 year female is approximately distributed with a mean of 118mmHg and a standard deviation of 12mmhg... A) what is the proportion of girls would you expect to have blood pressure between 112mmHg and 124mmHg... B) if you were to select a sample of 16 girls and obtain systolic blood pressure, what proportion of such sample would you expect between 112 mmHg and 124mmHg​

Answer 1

a) 0.383

b) 0.375

Explanation:

a) Calculate each z-score.

z = (x − μ) / σ

z₁ = (112 − 118) / 12 = -0.5

z₂ = (124 − 118) / 12 = 0.5

Use a calculator or z-score table to find the probability.

P(-0.5 < Z < 0.5) = 0.6915 − 0.3085 = 0.383

b) 0.383 × 16 ≈ 6. So the expected proportion would be 6/16 = 0.375.