The provincial transportation department is studying traffic patterns on one of the busiest highways in the province.As part of the study,the department needs to estimate the average number of vehicles that pass an intersection each day.A random sample of 64 days gives us a sample mean of 14,205 cars.Historically,the population standard deviation has been approximately 1,010 cars.What is the 92% confidence interval estimate of $\mu$
,the mean number of cars passing the intersection?
A)[12,438,15,972]
B)[14,028,14,382]
C)[12,189,14,221]
D)[13,984,14,426]
E)[14,183,14,227]

Question

Quizplus · Accepted Answer

The 92% confidence interval can be calculated using the formula for the confidence interval of the mean when the population standard deviation is known: $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. Given $\bar{x} = 14,205$, $\sigma = 1,010$, and $n = 64$, and knowing that the Z-score for a 92% confidence level is approximately 1.75, we calculate the margin of error and then the interval, which results in the interval [13,984, 14,426].

The Provincial Transportation Department Is Studying Traffic Patterns on One μ\muμ

The Provincial Transportation Department Is Studying Traffic Patterns on One $\mu$