Question

If np greater than or equals 5np≥5 and nq greater than or equals 5nq≥5 , estimate Upper P left parenthesis fewer than 2 right parenthesisP(fewer than 2) with nequals=13 and pequals=0.4by using the normal distribution as an approximation to the binomial distribution; if npless than<5 or nqless than< 5, then state that the normal approximation is not suitable.

Answer 1

Solution :

Given that,

n * p = 13 * 0.4 = 5.2

n * q = 13 * 0.6 = 7.8

The normal approximation is suitable .

Using binomial distribution,

= n * p = 13 * 0.4 = 5.2

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

Using continuity correction ,

= P((x - ) / < (1.5 - 5.2) / 1.7664)

= P(z < -2.09)

= 0.0183

Probability = 0.0183