Let x be a binomial random variable with n=50 and p=.3.The probability of less than or equal to 13 successes, when using the normal approximation for binomial is most closely reflected by ________.
A)-0.6172
B)0.3086
C)3.240
D)0.3217
E)-0.23224

Question

Quizplus · Accepted Answer

To use the normal approximation for a binomial distribution, we need to check if np and n(1-p) are both greater than or equal to 10. In this case, np = 15 and n(1-p) = 35. Since both are greater than 10, we can use the normal approximation with mean = np = 15 and standard deviation = sqrt(np(1-p)) = 2.872. To find the probability of less than or equal to 13 successes, we can use the normal distribution with continuity correction, as follows:
P(X ≤ 13) = P(X < 13.5)
z = (13.5 - 15) / 2.872 = -0.524
Using a standard normal table or calculator, we find P(Z < -0.524) = 0.3011
Therefore, the answer is D) 0.3217, which is the closest choice to 0.3011.

Let X Be a Binomial Random Variable with N=50 and P=.3.The