Question

Casino Carl loves flipping coins. In fact, he is preparing to flip a coin 50 times and track how many heads he gets (from zero to 50).

Use the normal approximation to find the probability Carl gets 20 heads or less from his 50 flips?

Answer 1

P(X < A) = P(Z < (A - mean)/standard deviation)

Sample size, n = 50

P(head), p= 0.5

q = 1 - p = 0.5

Mean = np

= 50 x 0.5

= 25

Standard deviation =

npq

=

V50 x 0.5 x 0.5

= 3.5355

P(Carl get 20 heads or less) = P(X $\small \leq$ 20)

= P(Z < (20.5 - 25)/3.5355) {with continuity correction}

= P(Z < -1.27)

= 0.1020