Question

A machine is used to fill bags with a popular brand of trail mix.

Answer 1

The least weight of a bag in the top 5 percent of the distribution is; 246

From the complete question below, we are given;

Population mean; μ = 240

Population standard deviation; σ = 3

Z-score formula is;

z = (x' - μ)/σ

• Now, we want to find the least weight in the top 5 of the distribution and as such we will use;

1 - 0.05/2 = 0.025 as significance level

Z-score at significance level of 0.025 is 1.96

Thus;

1.96 = (x' - 240)/3

3 × 1.96 = x' - 240

x' = 240 + 5.88

x' = 245.88

Approximating to a whole number gives;

x' = 246

Complete question is;

A machine is used to fill bags with a popular brand of trail mix. The machine is calibrated so the distribution of the weights of the bags of trail mix is normal, with mean 240 grams and standard deviation 3 grams. Of the following, which is the least weight of a bag in the top 5 percent of the distribution?

Read more about z-score at; brainly.com/question/25638875