The approximate range is 5.68 to 11.80 minutes.
To approximate the range in which the average commute time for the 1,000 employees is highly likely to fall, we can use the concept of confidence intervals.
Since the sample size is small (17 employees), we can assume that the population follows a normal distribution. We can calculate a 95% confidence interval, which is a common choice for estimating the true population mean.
To calculate the confidence interval, we need the mean and standard deviation of the sample. Unfortunately, the question doesn't provide this information. However, we can use the mean and standard deviation provided in example 1.18.
Using the sample mean commute time of 8.74 minutes and the sample standard deviation of 5.93 minutes, we can calculate the 95% confidence interval. The formula for the confidence interval is:
Confidence Interval = Sample Mean +/- (Critical Value * Standard Error)
To find the critical value for a 95% confidence interval, we can refer to the t-distribution table. With a sample size of 17, the number of degrees of freedom is 16.
The critical value for a 95% confidence interval with 16 degrees of freedom is approximately 2.13.
The standard error can be calculated by dividing the sample standard deviation by the square root of the sample size (5.93 / sqrt(17) = 1.44). Plugging the values into the confidence interval formula, we get:
Confidence Interval = 8.74 +/- (2.13 * 1.44) = 8.74 +/- 3.06
Therefore, the approximate range in which the average commute time for the 1,000 employees is highly likely to fall is 5.68 to 11.80 minutes.