Question

The weight of oranges growing in an orchard is normally distributed with a mean weight of 3.5 oz. and a standard deviation of 0.5 oz. What is the probability that a randomly selected orange from the orchard weighs less than 3 oz., to the nearest thousandth?

Answer 1

To find the probability that a randomly selected orange weighs less than 3 oz, we can use the Z-score formula:

Z = (X - μ) / σ

Where:
X = 3 oz
μ = 3.5 oz
σ = 0.5 oz

Z = (3 - 3.5) / 0.5
Z = -1

Now, we need to find the probability corresponding to Z = -1 using a standard normal distribution table or a calculator.

The probability that a randomly selected orange weighs less than 3 oz is approximately 0.1587.

So, the probability is 0.159 to the nearest thousandth.