Question 1: Marks:4+2+2=8 a) Theprobability that a trainee will remain with a co
ID: 2915038 • Letter: Q
Question
Question 1: Marks:4+2+2=8
a) Theprobability that a trainee will remain with a company is 0.6. Theprobability that an employee earns more than Rs.10, 000 per year is0.5. The probability that an employee is a trainee who remainedwith the company or who earns more than Rs.10, 000 per year is 0.7.What is the probability that an employee earns more than Rs.10, 000per year given that he is a trainee who stayed with thecompany.
b) The oddsagainst student X solving a Business statistics problem are 8 to 6,and odds in favour of student Y solving the problem are 14 to16.
Question2: Marks:1+3+2+3+1= 10
For the frequency distribution given below:
Length of Service
No of employees
7.5-7.9
6
8.0-8.4
22
8.5-8.9
36
9.0-9.4
18
9.5-9.9
14
10.0-10.4
4
Calculate
(i) Mean
(ii) Standard deviation
(iii) Co-efficient of Variation
(iv) Mean Deviation (from median)
(v) Range
Question3: Marks: 2+2=4
a) How many distinct four-digitnumbers can be performed from the following integers 1, 2, 3,4,5,6if each integer is used only once?
b) What would be the shape andname of the frequency distribution if
Question4: Marks:2+6=8
a) Describe the situation in whichtwo variables are perfect positively correlated?
b) The cost of output at a factoryis thought to depend on the number of units produced. Data havebeen collected for the number of units produced each month in thelast six months, and the associated costs, as follows;
Output
(‘000s of units) X
Cost
($’000) Y
2
9
3
11
1
7
4
13
3
11
5
15
Calculate the correlation coefficient and comment on yourresult.
Length of Service
No of employees
7.5-7.9
6
8.0-8.4
22
8.5-8.9
36
9.0-9.4
18
9.5-9.9
14
10.0-10.4
4
Explanation / Answer
The probability that a trainee will remain with a companyis 0.6. P(R) = 0.6 ----------------- The probability that an employee earns more than Rs.10, 000 peryear is 0.5 P(10K) = 0.5 ----------------- The probability that an employee is a trainee who remained with thecompany or who earns more than Rs.10, 000 per year is 0.7 P(R or 10K) = 0.7 ---------------------------- What is the probability that an employee earns more than Rs.10, 000per year given that he is a trainee who stayed with thecompany. P(10K | R) = P(10K and R)/P(R) --- Note: P(10K and R) = P(R)+P(10K)-P(10K or R) = 0.6+0.5-0.7 =0.4 ---------- Therefore P(10K |R) = 0.4/0.6 = 2/3
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