1 Determine whether of not the random variable Y is a binomial rando.pdf

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X is the number of correct guesses by a subject in an ESP test where a psychologist viewed 20 cards with different shapes and the subject guessed the shape. (1) If the subject is guessing, X follows a binomial distribution with n = 20 and p = 1/4. (2) The mean of X is μ = np = 5 and the standard deviation is σ = √np(1-p) = 2. (3) The probability of guessing more than 8 shapes correctly is small, casting doubt on the assumption that the subject was simply guessing.

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1 Determine whether of not the random variable Y is a binomial random variable. If so, give
the values of n and p.
2. In a test for ESP, a psycologist looks at a card that is hidden from the subject. Each card
contains either a star, a circio, a square of a hexagram. As the psycologist looks at each of 20
cards in turn, the subject names the shape on the card. Let X be the number of correct responses
by the subject.
(a) What is the distribution of X if the subject is guessing?
(b) Find Ix and ox.
(c) Suppose the subject guesses more than 8 figures correctly. Use the binomial tables to find the
probability that this happens. Does the probability cast doubt on the assumption that he is
guessing? 1. Determine whether or not the random variable X is a binomial random variable. If
so, give the values of n and p. (a) 4 cards are drawn from a 52 card deck without replacement, X
is the number of aces. (b) Joe plays pick 3 every day for a year. X is the number of times that he
wins. 2. In a test for ESP, a psycologist looks at a card that is hidden from the subject. Each card
contains either a star, a circle, a square or a hexagram. As the psycologist looks at each of 20
cards in turn, the subject names the shape on the card. Let X be the number of correct responses
by the subject. (a) What is the distribution of X if the subject is guessing? (b) Find X and X. (c)
Suppose the subject guesses more than 8 figures correctly. Use the binomial tables to find the
probability that this happens. Does the probability cast doubt on the assumption that he is
guessing?

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