The owner of a large shopping center is besieged with complaints concerning the shortage of parking space.He feels that the 1000 spaces are adequate.In an effort to address the problem,he obtains a sample of the average number of cars on the parking lot during prime hours.The sample of 40 has a mean of 952.Assume a population standard deviation of 396.The 95% confidence interval estimate for prime hour parking is:
A) 889.36 to 932.60.
B) 932.60 to 971.40.
C) 829.28 to 1074.72.
D) 849.00 to 1054.99.
E) 952.00 to 1052.00.

Question

Quizplus · Accepted Answer

The 95% confidence interval for the mean number of cars during prime hours can be calculated using the formula for the confidence interval of the mean with known population standard deviation: $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the confidence level (1.96 for 95%), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values ($\bar{x} = 952$, $\sigma = 396$, $n = 40$), we get the interval $952 \pm 1.96 \times \frac{396}{\sqrt{40}}$, which calculates to approximately $829.28$ to $1074.72$.

The Owner of a Large Shopping Center Is Besieged with Complaints