Question

If np greater than or equals 5 and nq greater than or equals 5​, estimate Upper P left parenthesis fewer than 5 right parenthesis with n=13 and p=0.4 by using the normal distribution as an approximation to the binomial​ distribution; if np less than 5 or nq less than​5, then state that the normal approximation is not suitable.

Answer 1

Solution :

n = 13

p = 0.4

q = 0.6

np = 13 * 0.4 = 5.2

nq = 13 * 0.6 = 7.8

Here , np > 5 and nq > 5

The normal approximation is suitable.

Using binomial distribution,

= n * p = 5.2

= n * p * q = 13 * 0.4 * 0.6 = 1.7664

Using continuity correction ,

= P((x - ) / < (4.5 - 5.2) / 1.76644.5-5.2)

= P(z < -0.40)

= 0.3446

Probability = 0.3446