A bus company official wanted to estimate the mean time for the trip between two cities. A random sample of such trips gave a mean of 152 minutes and a standard deviation of 12 minutes. Construct a 98% confidence interval for the population mean time.

To construct a confidence interval for the population mean time, we can use a formula for confidence intervals for a normal distribution when the population standard deviation is known.

The formula for a confidence interval is:

CI = sample mean ± (z-score) * (standard deviation / √sample size)

We are given the following information:
Sample mean (x̄) = 152 minutes
Standard deviation (σ) = 12 minutes
Confidence level = 98% (α = 0.02)

First, we need to find the z-score corresponding to the desired confidence level. We can look up this value in a standard normal distribution table or use statistical software.

Since we want a 98% confidence interval, the α (significance level) is 1 - 0.98 = 0.02. Dividing this by 2 (since it is divided equally between the two tails), we have α/2 = 0.01. The corresponding z-score for a 0.01 area in the tails is approximately 2.33.

Now we can plug all the values into the formula to calculate the confidence interval:

CI = 152 ± (2.33) * (12 / √n)

To find the sample size (n), we would need additional information about the random sample of trips. If the sample size is not given, we cannot provide an exact confidence interval. However, we can still explain the process and formula for constructing the interval.

So, to summarize:
The 98% confidence interval for the population mean time is calculated using the formula:
CI = 152 ± (2.33) * (12 / √n)

Please provide the sample size (n) to get the specific confidence interval.