If np is greater than or equal to 5 and nq is greater than of equal to 5, estimate P(fewer than 2)with n=14 and p=0.4 by using the normal distribution as an approximation to the binomial distribution

Question

...If np<5 or nq<5 then state that the normal approximation is not suitable

Answer 1

mean = np = 5.6 > 5

std dev = sqrt( npq) = sqrt( 14 * 0.4 * 0.6) = 1.83 < 5

Prob ( 1.5 < x < 2.5) <--- continuity correction

=Prob ( (1.5 - 5.6)/1.83 < z < (2.5 - 5.6)/1.83))

=Prob ( -2.2363 < z < -1.693989...)

=Prob( z< -1.693989... ) - Prob(z < -2.2363) =

= 0.045142 - 0.012666

=0.032476 = 3.2476%