Suppose that we\'ve deeded to test Clara, who works at the Psychic Center, to se

Question

Suppose that we've deeded to test Clara, who works at the Psychic Center, to see if she really has psychic abilities. While talking to her on the phone, well thoroughly shuffle a standard deck of 52 cards (which is made up of 13 hearts, 13 spades, 13 diamonds, and 13 dubs) and draw one card at random. Well ask Clara to name the suit (heart spade, diamond, or club) of the card we drew. After getting her guess, well return the card to the deck, thoroughly shuffle the deck, draw another card, and get her guess tor the suit of this second card Well repeat this process until we've drawn a total of 16 cards and gotten her suit guesses tor each. Assume that Clara is not clairvoyant, that is. assume that she randomly guesses on each card. Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the moan of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

Explanation / Answer

Each time prob for Clara guess right is the same as draw is with replacement.

That the events consist of independent Bernoulli trials with n =18, p = 1/4

q = 3/4

Hence the no of cards Clara guesses follow a Binomial distribution with X taking values as

0, 1, 2,3,,,,,,,,18

Mean = mean of binomial = np = 18/4 = 4.50

Variance = npq = 3.375

Hence std dev = 1.837

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