According to the Bureau of Labor Statistics it takes an average of 16 weeks for young workers to find a new job. Assume that the probability distribution is normal and that the standard deviation is two weeks. What is the probability that 20 young workers average less than 15 weeks to find a job?
A) 0.0225
B) 0.0450
C) 0.0375
D) 0.0127

Question

Quizplus · Accepted Answer

The probability can be found using the formula for the z-score in a normal distribution, which is $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Here, $\bar{x} = 15$, $\mu = 16$, $\sigma = 2$, and $n = 20$. Plugging these values into the formula gives $z = \frac{15 - 16}{2/\sqrt{20}} = \frac{-1}{2/\sqrt{20}} = \frac{-1}{0.4472} = -2.236$. Looking up this z-score in a standard normal distribution table or using a calculator gives a probability of approximately 0.0127.

According to the Bureau of Labor Statistics It Takes an Average