# a) Binomial method: Pr(r) = 0.5 r × 0.5(20 – r) × 20Cr. This gives probabilities of 15, 16,etc….

a) Binomial method: Pr(r) = 0.5r × 0.5(20−r) × 20Cr. This gives probabilities of 15, 16,etc. heads of 0.0148, 0.0046, etc., which total 0.0207 or 2.1%. By the Normalapproximation, r ~ N(10,5) and z = (14.5 − 10)/√5 = 2.01. The area in the tail
is then 2.22%, not far off the correct value (a 10% error). Note that nP = 10 n(1 − P).
(b) Binomial method: Pr(5 or 6 heads) = 0.302 + 0.118 = 0.420 or 42%. By theNormal, r ~ N(4.2, 1.26), z = 0.267 and the area is 39.36%, still reasonably closeto the correct answer despite the fact that n(1 − P) = 1.8.
(c) By similar methods the answers are 11.8% (Binomial) and 12.3% (Normal).

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