Question

The weight of oranges growing in an orchard is normally distributed with a mean weight of 7.5 oz. and a standard deviation of 0.5 oz. What percentage of the oranges from the orchard weigh between 8 oz. and 9 oz., to the nearest tenth?

Answer 1

Let X ~ N(7.5, 0.5^2). Compute z-scores:
z1 = (8−7.5)/0.5 = 1.0, z2 = (9−7.5)/0.5 = 3.0.

P(8 ≤ X ≤ 9) = Φ(3.0) − Φ(1.0) ≈ 0.998650 − 0.841345 = 0.157305 ≈ 15.7%.