When you flip a coin, the probability of its landing on each side is p = q = 1/2 in Equations 27-2 and 27 3. If you flip it n times, the expected number of heads equals the expected number of tails = np = nq = 1/2n. The expected standard deviation for n flips is σn = √npq. From Table 4-1, we expect that 68.3% of the results will lie within ± 1σn and 95.5% of the results will lie within ± 2σn.
(a) Find the expected standard deviation for the number of heads in 1 000 coin flips.
(b) By interpolation in Table 4-1, find the value of z that includes 90% of the area of the Gaussian curve. We expect that 90% of the results will lie within this number of standard deviations from the mean.
(c) If you repeat the 1 000 coin flips many times, what is the expected range for the number of heads that includes 90% of the results? (For example, your answer might be, "The range 490 to 510 will be observed 90% of the time.")