Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-A certain question on a test is answered correctly by 22% of the respondents. Estimate the probability that among the next 150 responses there will be at most 40 correct answers.
A) 0.1003
B) 0.0694
C) 0.8997
D) 0.9306

Question

Quizplus · Accepted Answer

Using the normal approximation to the binomial distribution, we calculate the mean (np) and standard deviation (sqrt(np(1-p))) for n=150 and p=0.22. Then, we find the z-score for 40.5 (continuity correction) and use the standard normal distribution to find the probability. The closest probability is 0.9306.

Estimate the Indicated Probability by Using the Normal Distribution as an Approximation