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

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph