Given that X is a binomial random variable, the binomial probability P(X $\le$ x) is approximated by the area under a normal curve to the left of:
A) x .
B) - x
C) x + 0.5 .
D) x - 0.5 .

Question

Given that X is a binomial random variable, the binomial probability P(X $\le$ x) is approximated by the area under a normal curve to the left of: 
A)  x . 
B)  - x 
C) x + 0.5 . 
D) x - 0.5 .

Quizplus · Accepted Answer

When approximating a binomial distribution with a normal distribution, we use the continuity correction, which involves adding or subtracting 0.5 from the x-value. This is because the binomial distribution is discrete, while the normal distribution is continuous. To find the area to the left of x using a normal distribution, we need to use the z-score corresponding to x+0.5, which is the midpoint between x and x+1. Therefore, the answer is C, x+0.5.

Given That X Is a Binomial Random Variable, the Binomial ≤\le≤

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