Given that X is a binomial random variable with very large n,the binomial probability P(X = 5)is approximated by the area under a normal curve between
A)5 and 5
B)4 and 6
C)4.5 and 5.5
D)None of these choices.

Question

Quizplus · Accepted Answer

When n is large, the binomial distribution can be approximated by a normal distribution with mean μ = np and standard deviation σ = √(np(1-p)). The continuity correction can be applied to approximate the probability of X = 5 as the area under the normal curve between 4.5 and 5.5. This is because we are looking for the probability that X takes on a specific value (5) and not a range of values. Option A is incorrect because the area under a normal curve at a specific point is always zero. Option B is incorrect because it is too broad for the specific probability we are looking for. Option D is incorrect because there is a best choice among the options given.

Given That X Is a Binomial Random Variable with Very