Answer to Question #219745 in Statistics and Probability for sai

Question

Professional basketball player Josh Richardson has a​ free-throw success rate of 80​%. Suppose Richardson takes as many free throws as he can in one minute. Why would it be inappropriate to use the binomial model to find the probability that he makes at least 7 shots in one​ minute? What condition or conditions for use of the binomial model is or are not​ met?

What condition or conditions for use of the binomial model is or are not​ met? Select all that apply.

It is inappropriate or appropriate to use the binomial model to find the probability because some,no or all binomial model conditions are met.

Answer 1

A binomial experiment

1. The experiment consists of a sequence of $n$ trials, where $n$ is fixed in advance of the experiment:

2. Each trial can result in one of the same two possible outcomes: success or failure.

3. The trials are independent.

4. The probability of success $P(S)$ is constant from trial to trial: $p=constant.$

A. There is not a fixed number of trials because Richardson can take any number of shots in one minute. True.

Condition 1 is not met.

B. There are more than two outcomes possible because Richardson can make any number of shots in one minute. False.

Since each trial can result in one of the same two possible outcomes: success or failure, then Condition 2 is met.

C. There is not a fixed number of trials because the number of shots was arbitrarily chosen before

starting. False.

Richardson takes as many free throws as he can in one minute. We suppose that the number of shots cannot be arbitrarily chosen before starting.

Therefore this is not a reason for non-fulfillment of the Condition 1.

D. The probability of success is not the same at each trial. False.

The probability of success $P(S)$ is constant from trial to trial: $p=0.8.$

E. There are more than two outcomes possible because Richardson will take at least 7 shots. False.

Each trial can result in one of the same two possible outcomes: success or failure.

F. All conditions for the binomial model are met. False.

Condition 1 is not met.

There is not a fixed number of trials because Richardson can take any number of shots in one minute.