Question

The amount of time that it takes a randomly selected employee at a large company to complete a certain task follows a normal distribution with mean 110 seconds and standard deviation 22 seconds. The 15% of employees that take the longest amount of time to complete the task are to be given remedial training. Find the value of the completion time that separates the longest 15% of completion times from the fastest 85%. (i.e. find the 85^th percentile.)

Answer 1

X ~ N ( µ = 110 , σ = 22 )
P ( X < x ) = 85% = 0.85
To find the value of x
Looking for the probability 0.85 in standard normal table to calculate Z score = 1.0364
Z = ( X - µ ) / σ
1.0364 = ( X - 110 ) / 22
X = 132.8008 ≈ 133

P ( X < 132.8008 ) = 0.85