Imagine that you are the manager of an engineering department that processes requests for quotations for new designs. Your past experience indicates that you receive 7 requests per month. What is the probability that you will receive more than 4 requests next month? The average time it takes one of your engineers to process such a request is 30 hours, with a range of 20 to 60. How many engineers should you have to be able to complete at least 90% of the work each month (everyone works 160 hours per month) ?

Question

Mathematics

Duckling

12 November, 16:34

Imagine that you are the manager of an engineering department that processes requests for quotations for new designs. Your past experience indicates that you receive 7 requests per month. What is the probability that you will receive more than 4 requests next month? The average time it takes one of your engineers to process such a request is 30 hours, with a range of 20 to 60. How many engineers should you have to be able to complete at least 90% of the work each month (everyone works 160 hours per month) ?

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Andre Todd · Answer 1

Step-by-step explanation:

Requests for quotations is governed by poisson distribution.

P (x>4) = 1 - P (<4)

= 1 -.172992

=.8270

To find out time required to process the request we proceed as follows

average time taken = 30 hours

range of time required 20 to 60 = 40

standard deviation σ = 40 / 4 (Range rule of Thumb)

= 10

Margin of error = 90%

So α =.05

z = 1.96 (normal distribution)

E² = (Z_α / 2) ² σ ² / n

(.90) ² = (1.96) ² x 10² / n

n = 474

required no = 474