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------------------------------------------------ Consider the following integer programming (IP) problem:

Maximize: [tex]7x_1 + 28x_2 - 12x_3 + 15x_4 + 5x_5[/tex]

Subject to: [tex]50x_1 - 70x_2 + 40x_3 + 30x_4 - 30x_5 \leq 100[/tex]

Which of the following conditions must be met in order for the Central Limit Theorem to apply? (Select all that apply.)

A. Each observation in our sample is independent of the other observations in our sample.
B. The sample size is small.
C. The population is not normally distributed.
D. The population standard deviation is known.

The Central Limit Theorem (CLT) applies when the observations in the sample are independent and the population is not necessarily normally distributed.

Explanation:

The Central Limit Theorem (CLT) applies when certain conditions are met. In this case, the conditions are:

Each observation in the sample should be independent of the other observations.
The sample size should be large.
The population does not have to be normally distributed.
The population standard deviation is not required to be known.

So, the correct conditions are a) Each observation in our sample is independent of the other observations in our sample, and c) The population is not normally distributed.

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