Question

A production line packages 3,000 boxes of cereal per hour. Quality control technicians randomly sample ten per hour and weigh them. The boxes are classified as underweight or not. X, the number of underweight boxes will be approximately ___________distributed.

Answer 1

Answer:

The boxes are classified as underweight or not. X, the number of underweight boxes will be approximately ___normally___distributed

Step-by-step explanation:

For a normal distribution the sample size must be less than or equal to 30.

The central limit theorem states that if a variable X from a population has a mean u and a finite variance σ² then the sampling distribution of the sample mean x bar approaches  a normal distribution with mean u and variance σ²/n as the sample size n approaches infinity.

In the given question the sample size n= 10 and population size N= 3000.

Here n < 30 . But if the population is normal this theorem holds true for sample size n < 30.

Answer 2

The number of underweight boxes should be normally distributed.

What is a normal distribution?

It is the distribution where the sample size should be lower than or equal to 30

Since the size of the sample is n = 10 and the size of the population is N = 3000

So here n should be less than 30

Therefore, it is normally distribution.

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