The R# Medical Centre undertook a survey to determine the average waiting time of patients in the surgery before they saw a doctor. From 14 responses, the average and standard deviation of the waiting times was found to be 26.6 and 16.37 minutes, respectively. Assuming the information was collected through a random sample and that the waiting time is approximately normally distributed, calculate a 95% confidence interval for the mean waiting time at the medical centre. State the lower bound (in minutes) correct to 3 decimal places.

To calculate a 95% confidence interval for the mean waiting time, we will use the formula for the confidence interval:

CI = x̄ ± Z * (σ/√n)

where: x̄ is the sample mean, Z is the Z-score (for a 95% confidence interval, Z = 1.96), σ is the standard deviation, and n is the sample size.

Given in the problem, we have: x̄ = 26.6 minutes, σ = 16.37 minutes, and n = 14.

Substituting these values into the formula, we get:

CI = 26.6 ± 1.96 * (16.37/√14)

To find the lower bound, we subtract the second term from the mean:

Lower bound = 26.6 - 1.96 * (16.37/√14)

Now, calculate the value inside the parentheses:

= 26.6 - 1.96 * (16.37/3.74) = 26.6 - 1.96 * 4.38 = 26.6 - 8.58

So, the lower bound of the 95% confidence interval for the mean waiting time is approximately 18.02 minutes, correct to 3 decimal places.