Question

For males in a certain town, the systolic blood pressure is normally distributed with a mean of 130 and a standard deviation of 7. What is the probability that a randomly selected male's systolic blood pressure will be between 114 and 119, to the nearest thousandth?

Answer 1

Let X ~ N(130, 7^2). Compute z-scores:
z1 = (114−130)/7 = −16/7 ≈ −2.2857
z2 = (119−130)/7 = −11/7 ≈ −1.5714

P(114 ≤ X ≤ 119) = Φ(−1.5714) − Φ(−2.2857) ≈ 0.05805 − 0.01113 ≈ 0.04692

Rounded to the nearest thousandth: 0.047.