Question

If np 25 and nq 25, estimate P(at least 8) with n= 13 and p=0.5 by using the normal distribution as an approximation to the binomial distribution, if np < 5 or ng <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 O A. P(at least 8) = (Round to three decimal places as needed.) OB. The normal distribution cannot be used.

Answer 1

Given:

n = 13, p = 0.5

q = 1-p = 1-0.5 = 0.5

Requirement for a normal approximation for the Binomial distribution:

np =13*0.5= 6.5

nq =13*0.5=6.5

Both np and nq are greater than 5.

So Condition satisfied.

Find: P(at least 8)

P(at least 8) = P(X =8) + P(X =9) + P(X =10) + P(X =11) + P(X =12) + P(X =13)

Therefore, the probability mass function of the binomial distribution is as follows:

.............................X = 0,1,2,3.........................n

P(X) = CM * p * q-1

Therefore,

P(at least 8) = 0.1571 + 0.0873 +0.0349+0.0095 + 0.0016 + 0.0001

P(at least 8) = 0.291

ANSWER: A

P(at least 8) = 0.291