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 118 headsminus− that's 59% heads.

1 a)	Use the Normal model to approximate the Binomial to determine the probability of spinning a fair coin 200 times and getting at least 118 heads.
1 b)	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

#1.
Here, μ = 100, σ = 7.0711 and x = 118. We need to compute P(X >= 118). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (118 - 100)/7.0711 = 2.55

Therefore,
P(X >= 118) = P(z <= (118 - 100)/7.0711)
= P(z >= 2.55)
= 1 - 0.9946 = 0.0054

2.
The probability of getting 118 heads in 200 tosses for a fair coin is significantly low which means the given coin is unfair.

Yes, it is unfair to use this coin.
No one will be willing to use this coin in sports event.