30 Jan You should include Excel output to support y
You should include Excel output to support your answers or reasoning as needed.
Q1 A sample of 200 executives is asked the question: “If you were given an offer by another company equal to or slightly better than your present position, would you remain with the company or take the other position?” The responses of the 200 executives in the survey were cross-classified with their length of service with the company, giving the results below:
Length of Service
Loyalty
< 1 1 - 5 6 - 10 > 10
Remain
10
30
5
75
Leave
25
15
10
30
(a) If an executive is picked at random, what is the probability that they are loyal (ie would remain with the company)? [2]
(b) If an executive is picked at random, what is the probability that they have been with the company for more than 10 years? [2]
(c) If an executive who has been with the company for more than 10 years is picked at random, what is the probability that they are loyal? [2]
(d) Which two of the above answers would you compare to judge whether Loyalty and Time of Service are independent? What does this comparison suggest? [2]
Q2 A consumer survey has derived the following probability distribution for the number of coffee cups drunk per day by adult New Zealanders:
no of cups
0
1
2
3
4
5
6
7
>7
male
0.40
0.34
0.12
0.05
0.04
0.03
0.01
0.01
0.00
female
0.47
0.35
0.08
0.06
0.02
0.01
0.01
0.00
0.00
(a) Separately for each gender, what is the probability of drinking more than two cups per day? [2]
Males:
Females:
(b) Calculate for each gender the average number of cups of coffee drunk per day. [3]
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