Question

Within what limits will the number of heads lie, with 95% probability, in 1000 tosses of a coin which is practically unbiased?​

Answer 1

Step-by-step explanation:

The evidence is pretty strong that the coin is biased. Using the normal approximation to the binomial distribution, the mean number of heads is np = 1000 x 0.5 = 500 and the standard deviation is sqrt(npq) = 16 (approx). 560 heads in 1000 tosses is almost 4 standard deviations (3.79) above the mean. The probability of tossing more than 560 heads in 1000 tosses is about .000075. Thus, it's very unlikely that p = 0.5 (= fair