A balanced coin is flipped 400 times. Determine the number [math]x[/math] such that the probability that the number of heads is between [math]200- x[/math] and [math]200 + x[/math] is approximately .80.

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Solution: B

The number of heads is approximately normally distributed with mean 200 and variance 200 *1/2 * 1/2 = 50. Then the probability that the number of heads is between [math]200-x [/math] and [math]200 + x [/math] is the probability that a standard normal variable is between [math]\frac{-x}{\sqrt{50}}[/math] and [math]\frac{x}{\sqrt{50}} [/math], which must equal 0.8. Since the 10^th percentile of a standard normal variable is approximately equal to -1.2816, this gives [math]x = 9.0622[/math].