Statistics help

Question

A coin is flipped 64 times. The number of heads observed over all the coin flips is a binomial random variable whose distribution is roughly normal. Use the normal approximation to compute the probability of flipping 30 heads?

Answer 1

64C30(1/2)^64 = probability of exactly 30 heads in 64 flips of a fair coin

probability of at least 30 heads is > 50% = .5 + Pr(30) + P(31) = .5+64C30(.5)^64 + 64C31(.5)^64

mean = np = 64(.5) = 32 heads

variance = npq = np(1-p) = 64/4 = 16

standard deviation =sqrnpq = sqr16 = 4

z score = (30-32)/4 = -2/4 =-1/2 = -.5

use z tables or a z calculator to find the

area under the normal curve from -.5 to +infinity = 69.146% chance of 30 or more heads