At least 140 heads in 256 flips

Question

A fair coin is flipped 256 times. Let X be the number of heads. Using the normal approximation, estimate P(X \ge 140).

Accepted Answer

Match a normal to the binomial: np = 256 	imes 0.5 = 128 and np(1-p) = 256 	imes 0.5 	imes 0.5 = 64, so X \approx N(128, 64) with standard deviation \sqrt{64} = 8. Standardize 140: z = \frac{140 - 128}{8} = \frac{12}{8} = 1.5. The upper-tail probability beyond z = 1.5 is P(Z \ge 1.5) \approx 0.0668, about 6.7%. Takeaway. Mean 128, sd 8, and z = 1.5 give P(X \ge 140) \approx 6.7\% under the normal approximation.

At least 140 heads in 256 flips

Your answer

More Statistics questions