The number of diners at a restaurant each day is recorded and a daily average is calculated every month (assume 30 days in a month). The number of diners each day has a mean of 110 and a standard...

The number of diners at a restaurant each day is recorded and a daily average is calculated every month (assume 30 days in a month). The number of diners each day has a mean of 110 and a standard deviation of 54, but does not necessarily follow a normal distribution.

The probability that a daily average over a given month is greater than x is 2.5%. Calculate x. Give your answer to 3 decimal places.