Question 1182192
mean is 1.5  hours and standard deviation is 15 minutes = .25 hours.
z-score for 85% area under the normal distribution curve to the left of it is equal to 1.03643338.
z-score formula is:
z = (x - m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation.
solve for raw score to get:
x = z * s + m = 1.03643338 * .25 + 1.5 = 1.759108345 hours.
that's how long the manager must be present.
this is what it looks like on the statistical calculator found at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>


<img src = "http://theo.x10hosting.com/2021/062704.jpg" >