Question

A candy company produces packets of candy every day. Each packet they produce has a slightly unique weight. The mean of the weights is 72g, and the variance of the weights is 16g.

What is the minimum weight of a packet of candy with a z-score of -0.6? (round to the nearest tenth as needed)

Answer 1

To determine the minimum weight of a packet of candy with a z-score of -0.6, we need to use the formula:

z = (x - μ) / σ

where:

z = -0.6 (given)

μ = 72g (given)

σ = sqrt(16g) = 4g (since variance = standard deviation squared)

Substituting the values in the formula, we get:

-0.6 = (x - 72) / 4

Multiplying both sides by 4, we get:

-2.4 = x - 72

Adding 72 to both sides, we get:

x = 69.6g

Therefore, the minimum weight of a packet of candy with a z-score of -0.6 is approximately 69.6g (rounded to the nearest tenth).