Recently, the average amount of time to foreclose on a house in the U.S. was reported to be 359 days. Assume that the standard deviation for this population is 90.4 days. A random sample of 42 homes that have completed the foreclosure process was selected. What is the probability that the sample average was less than 375 days?
A)0.5129
B)0.8749
C)0.6350
D)0.7264

Question

Quizplus · Accepted Answer

To find the probability that the sample average was less than 375 days, we use the formula for the z-score of a sample mean: $z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$, 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: $z = \frac{375 - 359}{\frac{90.4}{\sqrt{42}}}$. This calculation gives us a z-score, which we then look up in a standard normal distribution table or use a calculator to find the corresponding probability. The calculation results in a probability of 0.8749, indicating there's an 87.49% chance the sample average is less than 375 days.

Recently, the Average Amount of Time to Foreclose on a House