Based on all the data that has been collected so far the Bank Manager believes the mean (m) number of minutes to process a customer transaction is 8.0 minutes with a standard deviation (sigma) equal to 2.4 minutes.
Part One: Compute how often it will require 6 minutes or less to process a customer transaction using the normal distribution and the Normal Table (Table N).
x = 6
mean = 8.0
sigma = 2.4
Z = (x – mean) / sigma
Z =
The Tail Value from the Normal Table =
Part Two: Clearly explain the answer in Part One above for the Bank Manager.
Part Three: Compute how often it will require 6 minutes or more to process a customer transaction using the normal distribution and the Normal Table (Table N).
Since the total probability (percentage) needs to equal 1 (or 100%) this answer can be easily determined by subtracting the Tail Value found in Part One above from the number 1.
1 – Tail =
Part Four: Clearly explain the answer in Part Three above for the Bank Manager.
Part Five: Compute how often it will require 11 minutes or more to process a customer transaction using the normal distribution and the Normal Table (Table N).
x = 11
mean = 8.0
sigma = 2.4
Z = (x – mean) / sigma
Z =
From the Normal Table the Tail value =
Part Six: Clearly explain the answer in Part Five above for the Bank Manager.
Part Seven: Compute how often it will require 11 minutes or less to process a customer transaction using the normal distribution and the Normal Table (Table N).
Since the total probability (percentage) needs to equal 1 (or 100%) this answer can be easily determined by subtracting the Tail Value found in Part Five above from the number 1.
1 – Tail =
Part Eight: Clearly explain the answer in Part Seven above for the Bank Manager.