Question

Use the normal distribution to approximate the desired probability. A coin is tossed 21 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 15 tosses. What is the probability of being correct 15 or more times by guessing?

Use the normal distribution to approximate the desired probability. A coin is tossed 21 times. person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 15 tosses. What is the probability of being correct 15 or more times by guessing? SELECT ALL APPLICABLE CHOICES A A B) 3.792780% 4.392780% D) 3.809447% 4.592780% E) F) 4.642780% 4.042780% G) None of These

Answer 1

n=	21	p=	0.5000
here mean of distribution=μ=np=		10.5
and standard deviation σ=sqrt(np(1-p))=		2.2913
for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

probability =

P(X>14.5)

=

P(Z>1.75)=

1-P(Z<1.75)=

1-0.9596=

0.0404~4.04%

option F is correct