Question

The weight of cans of fruit is normally distributed with a mean of 1000 grams and a standard deviation of 50 grams. What is the probability that a can weighs between 1000 and 1100 grams?

Answer 1

There is a 47.72% probability that a can weighs between 1000 and 1100 grams.

Explanation:

z = (x - μ) / σ

z1 = (1000 - 1000) / 50 = 0

z2 = (1100 - 1000) / 50 = 2

z1 = 0 is 0.5000 (or 50% below).

P(Z < 2) = 0.9772 (from the table)

P(Z > 2) = 1 - 0.9772 = 0.0228

P(1000 < X < 1100) = P(z1 < Z < z2) = P(0 < Z < 2) = P(Z < 2) - P(Z < 0) = 0.9772 - 0.5000 = 0.4772 (or 47.72%)

So, there is a 47.72% probability that a can weighs between 1000 and 1100 grams.