Final answer:
To determine if Kerrich's coin gave too many heads to be balanced, we use the Normal approximation to find the probability of getting 5067 or more heads in 10,000 tosses. The answer is approximately 0.0019, which suggests that Kerrich's coin did not give too many heads to be balanced.
Step-by-step explanation:
To determine if Kerrich's coin gave too many heads to be balanced, we need to find the probability that a balanced coin would give 5067 or more heads in 10,000 tosses. This can be done using the Normal approximation.
First, we calculate the mean and standard deviation of a balanced coin's tosses. The mean is 0.5 (since the probability of heads is 0.5) and the standard deviation is sqrt(n*p*(1-p)). In this case, n = 10,000 and p = 0.5. So the standard deviation is sqrt(10,000 * 0.5 * (1-0.5)) which is approximately 50.
Next, we use the Normal approximation to find the probability of getting 5067 or more heads. We calculate the z-score using the formula: z = (x - mean) / standard deviation. In this case, x = 5067, mean = 10,000 * 0.5 = 5000, and standard deviation = 50. After calculating the z-score, we can look up the corresponding probability in the Z-table. The answer is approximately 0.0019, which corresponds to option D.