Question

Shortly after the introduction of a new​ coin, newspapers published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin 200 times and gotten 114 headsminus​that's 57​% heads. a right parenthesis font size decreased by 1 Use the Normal model to approximate the Binomial to determine the probability of spinning a fair coin 200 times and getting at least 114 heads. b right parenthesis font size decreased by 1 Do you think this is evidence that spinning this new coin is​ unfair? Would you be willing to use it at the beginning of a sports​ event? Explain.

Answer 1

When we tossed a fair coin, probability of getting a head is 0.5. So we have

n=200 and p=0.5

Since np = 100 and n(1-p) = 100 both are greater than 5 so we can use normal approximation here.

Using normal approximation, X has approximately normal distribution with mean and SD as follows:

The z-score for X= 114 -0.5 = 113.5 is

The probability of spinning a fair coin 200 times and getting at least 114 heads is

P(X >= 114) = P(X > 113.5) = P(z > 1.91) = 0.0281

Since above probability is less than 0.05 so it seems that coin is unfair. So you should not use it at the beginning of a sports event.