Question

If np≥5 and nq≥5, estimate P (more than 6 ) with n=11 and p=0.7 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( more than 6)= (Round to four decimal places as needed.)
B. The normal distribution cannot be used.

Answer 1

The normal approximation is not suitable.

Step-by-step explanation:

In order to estimateP(more than 6) withn=11andp=0.7 using the normal distribution as an approximation to the binomial distribution, we need to check if the conditions for the approximation are met. The conditions are np≥5andnq≥5. For this question, since n=11andp=0.7, we have np=11(0.7)=7.7 andnq=11(0.3)=3.3. Sincenq<5, the normal approximation is not suitable.