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Suppose that we ve decided to test Clara who works at the Psychic Center to...

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Suppose that we ve decided to test Clara who works at the Psychic Center to see if she really has psychic abilities While talking to her on the phone we ll thoroughly shuffle a standard deck of 52 cards which is made up of 13 hearts 13 spades 13 diamonds and 13 clubs and draw one card at random We ll ask Clara to name the suit heart spade diamond or club of the card we drew After getting her guess we ll return the card to the deck thoroughly shuffle the deck draw another card and get her guess for the suit of this second card We ll repeat this process until we ve drawn a total of 15 cards and gotten her suit guesses for each Assume that Clara is not clairvoyant that is assume that she randomly guesses on each card Answer the following If necessary consult a list of formulas a Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the mean of the relevant distribution that is the expectation of the relevant random variable Do not round your response 0 b Quantify the uncertainty of your estimate by giving the standard deviation of the distribution Round your response to at least three decimal places

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