Question

If np ≥5 and nq ≥​5, estimate P (at least 7) with n =13 and p=0.6 by using the normal distribution as an approximation to the binomial​ distribution; if np <5 or nq <​5, then state that the normal approximation is not suitable.

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

P (at least 7) =

​(Round to three decimal places as​ needed.)

B.

The normal distribution cannot be used.

Answer 1

Solution:

Given that,

P = 0.6

1 - P = 0.4

n = 13

Here, BIN ( n , P ) that is , BIN (13 , 0.6)

then,

n*p = 7.8 5

n(1- P) = 5.2 5

According to normal approximation binomial,

X Normal

Mean = = n*P = 7.8

Standard deviation = =n*p*(1-p) = 3.12

We using continuity correction factor

A)

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

P(x > 6.5) = 1 - P(x < 6.5)

= 1 - P((x - ) / < (6.5 - 7.8) / 3.12 )

= 1 - P(z < -0.74)

= 1 - 0.2296 ( using z-table)

= 0.7704

Probability = 0.7704