According to Bureau of Labor Statistics, 26.0% of the total part-time workforce in the U.S. was between the ages of 25 and 34 during a recent month. A random sample of 90 part-time employees was selected during this quarter. Using the normal approximation to the binomial distribution, what is the probability that fewer than 19 people from this sample were between the ages of 25 and 34?

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=90 and p=0.26. Then, we find the z-score for 18.5 (continuity correction) and use the standard normal distribution to find the probability. The closest probability to the calculated value is 0.1190.