Let x be a binomial random variable with n=50 and p=.3. The probability of less than or equal to13 successes,when using the normal approximation for binomial is ____ ____
A) -.6172
B).3086
C)3.240
D).2676
E)-.23224

Question

Quizplus · Accepted Answer

We need to use the normal approximation for binomial distribution, where the mean is np=15 and the standard deviation is sqrt(npq)=2.872.
We need to find P(x<=13) which is equivalent to finding P(z<=(13-15)/2.872) since we standardize the distribution using z-scores.
This gives us P(z<=-0.698) which we can find using a standard normal distribution table or calculator to be 0.2437.
Therefore the probability of less than or equal to 13 successes is 0.2437 or approximately 0.2676 (rounded to four decimal places).

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