Question

If npgreater than or equals5 and nqgreater than or equals​5, estimate Upper P left parenthesis at least 7 right parenthesis with nequals13 and pequals0.5 by using the normal distribution as an approximation to the binomial​ distribution; if npless than5 or nqless than​5, then state that the normal approximation is not suitable.

Answer 1

Solution :

Given that,

n * p = 13 * 0.5 = 6.5 > 5

n * q = 13 * 0.5 = 6.5 > 5

The normal approximation is not suitable .

= n * p = 13 * 0.5 = 6.5

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

Using continuity correction ,

P(x 6.5) = 1 - P(x   6.5)

= 1 - P[(x - ) / (6.5 - 6.5) / 1.8028]

= 1 -  P(z 0)  

= 1 - 0.5

= 0.5