Question

The weight of oranges growing in an orchard is normally distributed with a mean weight of 8 oz. and a standard deviation of 1.5 oz. What is the probability that a randomly selected orange from the orchard weighs more than 10 oz., to the nearest thousandth?

Answer 1

Let X ~ N(8, 1.5^2). Compute z = (10 − 8)/1.5 = 1.3333.
P(X > 10) = 1 − Φ(1.3333) ≈ 1 − 0.9088 = 0.0912.

To the nearest thousandth: 0.091.