14. The Association for Research and Enlightenment (ARE) in Virginia Beach, VA,
ID: 3302803 • Letter: 1
Question
14. The Association for Research and Enlightenment (ARE) in Virginia Beach, VA, offers daily demonstrations of a standard technique for testing extrasensory perception (ESP). A "sender" is seated before a box on which one of five symbols (plus, square, star, circle, wave) can n such a way bol that each symbol is equally likely to be illuminated. When a sym is illuminated, the sender concentrates on it and a "receiver" attempts to identify which symbol has been selected. The receiver indicates a symbol on the receiver's box, which sends a signal to the sender's box that cues it to select and illuminate another symbol. This process of illuminating, sending, and receiving a symbol is repeated 25 times. Each selection of a symbol to be illuminated is independent of the others. The receiver's score (for a set of 25 trials) is the number of symbols that s/he correctly identifies. For the purpose of this exercise, please suppose that ESP does not exist. (a) How many symbols should we expect the receiver to identify cor- rectly?Explanation / Answer
a. There are n=25 independent trials and probability of success (identifying correct symbol) is 1/5=0.2. The probability of success is constant throughout the trials. Thus, this accounts for binomial distribution, and one can expect the receiver to identify E=np=25*0.2= 5 symbols correctly.
b. P(x>7)=1-P(X<=7)=1-0.8909=0.1091 [Look into binomial table for p=0.2, n=25 and x=7, the table gives cumulative probability value]
c. P(X>=1)=1-P(X<1)=1-P(X=0)=1-20C0(0.1091)^0(1-0.1091)^20 [use binomial distribution formula, P(X,r)=nCr(p)^r(1-p)^n-r, where, p=0.1091 is the probability of success (indicative of ESP), n=20 is number of trials, r is the specific number of success in n trials].
=1-0.0992=0.9008
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