Question

The customer service manager of a company has tracked the number of customer complaints that she has received each day for the last 25 days. The data is:

• 0 complaints, 1 day
• 1 complaint, 2 days
• 2 complaints, 0 days
• 3 complaints, 2 days
• 4 complaints, 4 days
• 5 complaints, 1 day
• 6 complaints, 3 days
• 7 complaints, 3 days
• 8 complaints, 5 days
• 9 complaint, 3 days
• 10 complaints, 1 day

Based on this probability distribution, calculate:

1. The probability she will receive less than or equal to 6 complaints in a day.

Answer 1

Probability Distribution of X = Number of complaints is calculated as follows:

Number of complaints (x)	Frequency (f)	Probability (P(x)
0	1	1/25=0.04
1	2	2/25=0.08
2	0	0/25=0.00
3	2	2/25=0.08
4	4	4/25=0.16
5	1	1/25=0.04
6	3	3/25=0.12
7	3	3/25=0.12
8	5	5/25=0.20
9	3	3/25=0.12
10	1	1/25 = 0.04

P(X6) =P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)

= 0.04 + 0.08 + 0.00 + 0.08 + 0.16 + 0.04+ 0.12 = 0.52

So,

Answer is:

0.52