In the coin toss experiment, how many times must I toss it at least to make the frequency of the head appearing in the range of (0.4, 0.6) not less than 0.9? Determined by the central limit

Let it be at least n times, let x = (x 1+x2+...+xn)/n, x 1, x2, x3...xn is a sample of the whole x, p (x = 1) = 0.5, and x =/kloc-0.

Then x-pull is the frequency of frontal appearance, and the mathematical expectation and variance of x-pull are EX=0.5, DX= 1/4n.

p(0.4 & lt； X pulling force

2 φ (0.2 √ n)-1> if the probability of frontal appearance frequency in the range of (0.4, 0.6) is not less than 0.9; =0.9

φ(0.2√n)>=0.95, 0.2√n >= 1.65, so n >; =68.0625, so throw it at least 69 times.