Using technology, use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample. $n = 75 , p = 0.57 : P ( X \leq 47 )$
A) 0.8572
B) 0.1340
C) 0.8826
D) 0.8660

Question

Quizplus · Accepted Answer

Since n*p = 42.75 and n*(1-p) = 32.25 are both greater than or equal to 10, we can use the normal approximation to approximate the binomial distribution. We standardize the distribution by finding the z-score:

z = (47 - n*p) / sqrt(n*p*(1-p)) = (47 - 42.75) / sqrt(75 * 0.57 * 0.43) = 1.46

Using a standard normal distribution table or calculator, we find P(Z ≤ 1.46) = 0.8660. Therefore, the answer is D.

Using Technology, Use the Normal Approximation to Find the Indicated n=75,p=0.57:P(X≤47)n = 75 , p = 0.57 : P ( X \leq 47 )n=75,p=0.57:P(X≤47)

Using Technology, Use the Normal Approximation to Find the Indicated $n = 75 , p = 0.57 : P ( X \leq 47 )$