Use normal distribution to approximate desired probability

[dkf2006]

Use the normal distribution to approximate the desired probability.

Problem: A coin is tossed 20 times. A person who claims to have extrasensory perception is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the probability of being correct 14 or more times by guessing? Does this probability seem to verify her claim?

Thank you all for your answers. I made corrections on the question.

 

[pka]

I wonder why you titled this ‘normal distribution’?
Are you supposed to use a normal approximation?
If is easy to find the exact binomial probability: \(\displaystyle \sum\limits_{k = 14}^{20} {{20 \choose k}\left( {\frac{1}{2}} \right)^{20} }\)

 

[marcmtlca]

I believe the question is asking for the normal approximation to the binomial. The central limit theorem tells us that the binomial will converge to a normal distribution when the number of trials is large.

The thing is when you go from a discrete distribution to a continuous one you usually need to make an adjustment but i wont bother with that.

the mean, E(X) when X is a binomial random variable is n*p
and the variance is n*p(1-p)

your z value is therefore:

\(\displaystyle z=\frac{14-np}{\sqrt{np(1-p)}}\)

your answer would be \(\displaystyle 1-\Phi(z)\)