Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean of more than 404.5 is closest to _______.
A)0.0139
B)0.4861
C)0.4878
D)0.0122
E)0.5000

Question

Quizplus · Accepted Answer

The probability of drawing a sample with a mean of more than 404.5 can be found using the Z-score formula for a sample mean: $Z = \frac{\bar{X} - \mu}{\sigma/\sqrt{n}}$, where $\bar{X}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $Z = \frac{404.5 - 400}{24/\sqrt{144}} = \frac{4.5}{2} = 2.25$. Looking up 2.25 in the Z-table gives a right-tail probability of approximately 0.0122.

Suppose a Population Has a Mean of 400 and a Standard