In a test for ESP (extrasensory perception), a subject is told that cards the experimenter can see but the subject cannot contain a star, a circle, a wave, a triangle or a square. As the experimenter looks at each card in turn, the subject names the shape on the card. A subject who is just guessing has a one in four chance of guessing correctly on each card. A. The count of correct guesses in 20 cards has a binomial distribution. What are n and p?
B. What is the mean number of correct guesses in 20 cards for subjects who are just guessing?
C. What is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?

a) and

b) The mean number of correct guesses in 20 cards for subjects who are just guessing is 5.

c) 0.2023 = 20.23% probability of exactly 5 correct guesses in 20 cards if a subject is just guessing

Step-by-step explanation:

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 expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

A. The count of correct guesses in 20 cards has a binomial distribution. What are n and p?

20 cards mean that

A subject who is just guessing has a one in four chance of guessing correctly on each card, which means that

B. What is the mean number of correct guesses in 20 cards for subjects who are just guessing?

Expected value, so

The mean number of correct guesses in 20 cards for subjects who are just guessing is 5.

C. What is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?

This is P(X = 5). So

0.2023 = 20.23% probability of exactly 5 correct guesses in 20 cards if a subject is just guessing