Question

If np greater than or equals 5np≥5 and nq greater than or equals 5nq≥5​, estimate Upper P left parenthesis fewer than 3 right parenthesisP(fewer than 3) with nequals=1313 and pequals=0.50.5 by 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 :

n * p = 13 * 0.5 = 6.5 > 5

n * q = 13 * 0.5 = 6.5 > 5

the normal approximation is suitable .

Using binomial distribution,

= n * p = 13 * 0.5 = 6.5

= n * p * q = 13 * 0.5 * 0.5 = 1.8028

Using continuity correction ,

= P((x - ) / < (2.5 - 6.5) / 1.8028)

= P(z < -2.22)

= 0.0132

Probability = 0.0132