Question

A bank collects data on the number of loan applications filled incorrectly each day to construct a np-chart. Data from the previous 10 days indicate the following number of loan applications filled incorrectly per day in a sample size of 25 per day.

Day	Incorrect loan applications/day
1	5
2	7
3	6
4	5
5	8
6	4
7	4
8	5
9	5
10	6

Question 1. Calculate the average number of incorrect loan applications per sample and the corresponding standard deviation.
A. np-bar = 5.2; the standard deviation is = 2.2094
B. np-bar = 5.6; the standard deviation is = 2.0846
C. np-bar = 4.9; the standard deviation is = 1.9848
D. np-bar = 5.5; the standard deviation is = 2.0712

Question 2. Using +- 3-sigma limits, calculate the LCL and UCL for these data.

1. UCL = 10.855; LCL = 0
2. UCL = 11.854; LCL = 0
3. UCL = 11.288; LCL = 0
4. UCL = 11.714; LCL = 0

Answer 1

Since there are 55 defective items in 10 samples of smple size 25,

the fraction defective pbar = 55/25x10 = 0.22

1. npbar = 25x0.22 =5.5

SD = [ npbar ( 1-pbar)]^1/2 = [ 5.5 x(0.78)]^1/2 = 2.071

D is correct

2.Control limits

UCL = npbar + 3 [ npbar ( 1-pbar)]^1/2 = 5.5+ 3[ 5.5 x(0.78)]^1/2 = 11.7136

LCL = npbar - 3 [ npbar ( 1-pbar)]^1/2 = 5.5-3[ 5.5 x(0.78)]^1/2 =0 ( as defects can't be negative)

D is correct