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4. In 2008, Mars Inc. disclosed that 20% of the population of all M&M’s is orange....

4. In 2008, Mars Inc. disclosed that 20% of the population of all M&M’s is orange. Suppose we take repeated samples of size 50 of randomly selected M&M’s. What is the likelihood of having a sample that is at least 30% orange?

Math   Statistics-And-Probability   
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Answer #1

The distribution of the proportion of orange M&Ms in a sample of 50 M&Ms is obtained here as:

The probability / likelihood of having a sample that is at least 30% orange is computed here as:

P( p >= 0.3)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.0386 is the required probability here.

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