I need solution for tis all question
1). In a organization out of 200 employees, 40 are having their monthly salary more than Rs. 15000 and 120 of them are regular takers of alpha brand tea. Out of those 40 who are having their monthly salary more than Rs. 15000, 20 are regular takers of alpha brand tea. If a particular employee is selected what is the probability that he is having monthly salary more than Rs. 15000 if he is a regular taker of alpha brand tea.
2). Differentiate (X2- 2)(3X+1). X square
3).In a survey with a sample of 300 respondent the monthly income of respondents follows normal distribution with its mean and standard deviation as Rs. 15000 and Rs. 3,000 respectively. Assume the significance level as 0.10 and answer the following.
A). What is the probability that the monthly income is less than Rs. 12,000 Also find the number of respondent having income less than Rs. 12,000.
B). What is the probability that the monthly income is more than Rs. 16,000 Also find the number of respondents having income more than Rs. 16,000.
C). What is he probability that the monthly income is in between Rs. 10,000 and Rs. 17,000 Also find the number of respondent having income in between Rs. 10,000 and Rs. 17,000.
4). A company owns a lease on a certain property. It may sell the lease for Rs. 75,000 or may drill the said property for oil. Various possible drilling result are as under along with probabilities of happening and rupee consequence.
Possible result probability Rupee consequence
Dry well 0.10 -1,00,000
Gas well only 0.40 45,000
Oil and gas combination 0.30 98,000
Oil well 0.20 1,99,000
Draw a decision tree for the above problem and determine whether the company should drill or sell.
5). A production manager wishes to test the effect of 5 similar milling machines on the surface finish of small casting so he selected 5 such machines and conducted the experiment with four replication under Each machine as per completely randomized design and obtained and obtain the reading in microns as shown below.
A). State H0 and H1.
B). Perform the required ANOVA and state the interference at the significance level 0.05.
Machines
M1 M2 M3 M4 M5
25 10 40 27 15
Replication 30 20 30 20 8
16 33 49 35 45
36 42 22 48 34
6). Suppose a manufacturer can sell x items per week at a price P=30-0.001x rupees each when it cost, y=4x+1800 rupees to produce x items. Determine the number of items he should produce per week for maximum profit.
7). The rate of return (in percentage) of a product as a function of R&D expenditure (in lakhs of rupees) and annual advertising expenditure (in lakhs of rupees) for the past 7 years are summarized below . Design a regression model to forecast the rate of return of the product.
Rate of return R&D expenditure Annual advertising expenditure
(y) (X1) (X2)
12 12 30
15 16 50
14 18 65
18 20 75
17 18 80
15 25 95
20 30 105
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