A man claims to have extrasensory perception. As a test, a fair coin is flipped 28 times, and the man is asked to predict the outcome in advance. He gets 25 out of 28 correct. What is the probability that he would have done at least this well if he had no ESP?

Using the probability mass function we got:

And adding the probabilities we got:

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Let X the random variable of interest, on this case we now that:  

The probability mass function for the Binomial distribution is given as:  

Where (nCx) means combinatory and it's given by this formula:  

Solution to the problem

For a fair coin flip n=28 times we have the following distribution:

We want to find this probability:

Using the probability mass function we got:

And adding the probabilities we got:

graph them on a graphing calculator, press 2nd trace. select intersect. hit enter until it says answer. ti 84 works best

step-by-step explanation:

the answer is 150.6

step-by-step explanation:

you multiply .02 by 30 and get .6.

and then you multiply 5.00 by 30 and get 150.

hope this !