A company that makes rock and roll t-shirts has a printing problem that causes the band names to smear on 4% of the t-shirts. The daily production run is 2,000 t-shirts. What is the probability, if a sample of 100 t-shirts is checked, there will be smeared names on at most 4 t-shirts?

62.89% probability that there will be smeared names on at most 4 t-shirts

Step-by-step explanation:

For each shirt, there are only two possible outcomes. Either there will be smeared names, or there will not. The probability of there being smeared names on a shirt is independent of other shirts. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

4% of the shirts are smeared:

So

What is the probability, if a sample of 100 t-shirts is checked, there will be smeared names on at most 4 t-shirts?

This is when . So

62.89% probability that there will be smeared names on at most 4 t-shirts

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step-by-step explanation: