Question 10.6: Weights of bags of oranges are normally distributed with mea......
Weights of bags of oranges are normally distributed with mean 3 lbs and standard deviation 0.2 lb. The delivery to a supermarket is 350 bags at a time. Determine the following:
1. Standardize to a unit normal distribution.
2. What is the probability that a standard bag will weigh more than 3.5 lbs?
3. How many bags from a single delivery would be expected to weigh more than 3.5 lbs?
1. Z = X − μ/σ = X − 3/0.2.
2. Therefore, when X = 3.5, we have Z = 3.5 − 3/0.2 = 2.5.
For Z = 2.5, we have from the unit normal tables that
P(Z ≤ 2.50) = 0.9938 = P(X ≤ 3.5)
Therefore, P(X > 3.5) = 1 – P(X ≤ 3.5) = 1 – 0.9938 = 0.0062
3. The proportion of all bags that have a weight greater than 3.5 lbs is 0.0062, and so it would be expected that there are 350 ∗ 0.0062 = 2.17 bags with a weight > 3.5, and so in practical terms we would expect 2 bags to weigh more than 3.5 lbs.