3. In a study of ESP, a researcher looks at 500 randomly sorted cards bearing one of 5 shapes star, square, circle, wave and cross). The student subject cannot see the card or the researcher. For each card, the subject guesses the shape on the card that the researcher is looking at (presumably by ESP). The guesses from a student without ESP should be correct 1 out of 5 times by random chance alone (P = 0.2). X = the number of correct guesses out of n = 500 tries. a. Assuming the subject does not have ESP (P = 0.2), what are E ( P ) and o p for the sampling distribution of P = proportion of correct guesses out of n = 500 attempts. E ( P ): OP :. Based available information, is the sampling distribution for P = proportion of correct guesses out of n = 500 attempts approximately Normal? Explain your answer. 6.1 C . Based on the description above, scale the X-axis of the sampling distribution of P , derived on the assumption that the subject does NOT have ESP. Shade the area under the curve that corresponds to the probability P [P 2 0.24]. d. Use the Standard Normal Distribution to determine this probability