Question

in a test of ESP (extrasensory perception), the experimenter looks at cards that are hidden from the participant. Each card contains either a star, a circle, a wavy line, or a square. An experimenter looks at each of 100 cards in turn, and the participant tries to read the experimenter's mind and name the shape on each. The probability that the participant gets at least 30 correct if the participant does NOT have ESP and is just guessing is closest to:

Answer 1

n=

100

p=

0.2500

here mean of distribution=μ=np=		25.00
and standard deviation σ=sqrt(np(1-p))=		4.33
for normal distribution z score =(X-μ)/σx

therefore from normal approximation of binomial distribution and continuity correction:

probability that the participant gets at least 30 correct if the participant does NOT have ESP and is just guessing :

probability =P(X>29.5)=P(Z>(29.5-25)/4.33)=P(Z>1.04)=1-P(Z<1.04)=1-0.8508=0.1492