Does the estimate of a tolerance level of 68.26% of all patient waiting times provide evidence that at least two-thirds of all patients will have to wait less than 8 minutes?

Yes, because the upper limit is less Than 8 minutes

Explanation:

According to the empirical formula :

68.26% of data lies within 1 standard deviation from the mean;

Hence,

Mean ± 1(standard deviation)

The sample mean and sample standard deviation of the given data is :

Sample mean, xbar = Σx / n = 546 / 100 = 5.46

Sample standard deviation, s = 2.475 (Calculator)

The interval which lies within 68.26% (1 standard deviation is) ;

Lower = (5.460 - 2.475) = 2.985

Upper = (5.460 + 2.475) = 7.935

(2.985 ; 7.935)

Since the interval falls within ; (2.985 ; 7.935) whose upper level is less than 8 means patients will have to wait less Than 8 minutes.