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.
$n = 86 , p = 0.68 : P ( 54 \leq X \leq 61 )$
A) 0.6330
B) 0.1251
C) 0.7580
D) 0.2420

Question

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. 
$n = 86 , p = 0.68 : P ( 54 \leq X \leq 61 )$
A)  0.6330 
B)  0.1251 
C)  0.7580 
D)  0.2420

Quizplus · Accepted Answer

The correct answer is A.The mean of the binomial distribution is np = 86 * 0.68 = 58.48. The standard deviation of the binomial distribution is sqrt(np(1-p)) = sqrt(86 * 0.68 * 0.32) = 4.32. The z-scores for X = 54 and X = 61 are (54 - 58.48) / 4.32 = -1.04 and (61 - 58.48) / 4.32 = 0.59, respectively. The probability of 54 ≤ X ≤ 61 is the area under the normal curve between z = -1.04 and z = 0.59, which is 0.6330.

Use the Normal Approximation to Find the Indicated Probability n=86,p=0.68:P(54≤X≤61)n = 86 , p = 0.68 : P ( 54 \leq X \leq 61 )n=86,p=0.68:P(54≤X≤61)

Use the Normal Approximation to Find the Indicated Probability $n = 86 , p = 0.68 : P ( 54 \leq X \leq 61 )$