The probability that Shruti succeeds at any given free-throw is 80%, percent. She was curious how many free-throws she can expect to succeed in a sample of 12 free-throws.

She simulated 25 samples of 12 free-throws where each free-throw had a 0.8, point, 8 probability of being a success.

Shruti counted how many free-throws were successes in each simulated sample. Here are her results:

Use her results to estimate the probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

Give your answer as either a fraction or a decimal.

0.5584 probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

Step-by-step explanation:

For each free throw, there are only two possible outcomes. Either she makes it, or she does not. The probability of making a free throw is independent of other free throws. 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.

The probability that Shruti succeeds at any given free-throw is 80%, percent.

This means that

Sample of 12 free throws:

This means that

Use her results to estimate the probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

In which

0.5584 probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.