Question

The Chair of the Operations Management Department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic POM course are in control with regard to the number of students who fail the course. Accordingly, he randomly picked 100 final grades from last year for each instructor, with the following results:

GRADES FAILURES
Prof. A 100 12
Prof. B 100 1
Prof. C 100 11
Prof. D 100 16
What is the proportion of failures for Prof. A?
a. 0.10 7.
b. 0.12
c. 0.16
d. 0.01 8.
What is the average proportion of failures for these instructors?
a. 0.10
b. 0.12
c. 0.16
d. 0.01 9.
What is the standard deviation of the sampling distribution for the sample proportion of failures?
A. 0.0075
B. 0.03
C. 0.075
D. 0.3
E. 0.75

Answer 1

A) Professor A failure proportion = 0.12 ; B) Average = 0.1 ; C) σ = 0.055

Explanation:

1) Proportion of failures for Prof A : Failure / Total

= 12 / 100 = 0.12

2) Proportion of failures for Prof B : 1/ 100 = 0.01

Proportion of failures for Prof C : 11 / 100 = 0.11

Proportion of failures for Prof D = 16 / 11 = 0.16

Average proportional failure for all instructors :-

[ Prop (prof A) + Prop (prof B) + Prop (prof C) + Prop (prof D) ] / 4

(0.12 + 0.01+ 0.11 + 0.16 ) / 4 = 0.4 / 4 = 0.1

3) Standard Deviation (σ) = √ Σ (x - x')^2 / n , where x' = mean = 0.1

x x - x' (x - x')^2

0.12 0.02 0.0004

0.01 -0.09 0.0081

0.11 0.01 0.0001

0.16 0.06 0.0036

Σ = 0.0122

σ = √ 0.0122/ 4 = √0.00305 = 0.055