Question

If npgreater than or equals≥5 and nqgreater than or equals≥ 5, estimate Upper P left parenthesis at least 9 right parenthesisP(at least 9) with nequals=13 and pequals=0.5 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:

Given that,

P = 0.5

1 - P = 0.5

n = 13

Here, BIN ( n , P ) that is , BIN (13 , 0.5)

then,

n*p = 13*0.5 = 6.5 5

n(1- P) = 13*0.5 = 6.5 5

The normal approximation is suitable.

According to normal approximation binomial,

X Normal

Mean = = n*P = 6.5

Standard deviation = =n*p*(1-p) = 13*0.5*0.5 = 3.25

We using countinuity correction factor

P(X a ) = P(X > a - 0.5)

P(x > 8.5) = 1 - P(x < 8.5)

= 1 - P((x - ) / < (8.5 - 6.5) / 3.25)

= 1 - P(z < 1.109)

= 1 - 0.8663   

= 0.1337

Probability = 0.1337