Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is σ = 9 days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. The probability that the sample mean is less than 30 school days is ________.
A) 0.0918
B) 0.4129
C) 0.5871
D) 0.9088

Question

Quizplus · Accepted Answer

To find the probability that the sample mean is less than 30 days, we use the formula for the z-score: $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, 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, $\bar{x} = 30$, $\mu = 28$, $\sigma = 9$, and $n = 36$. Plugging these values into the formula gives $z = \frac{30 - 28}{9/\sqrt{36}} = \frac{2}{1.5} = 1.33$. Looking up 1.33 in the standard normal distribution table or using a calculator gives a probability of 0.9082, which rounds to 0.9088, indicating the probability that the sample mean is less than 30 days is 0.9088.

Over the Entire Six Years That Students Attend an Ohio