1. Solve the following system of equations

3x-2y+3z=8

2x+y-z=1

4x-3y+2z=4

2. A distribution is negatively skewed with the coefficient of skewness as -2.9. The value of mean and mode are 125 and 138, respectively. Find the variance of the distribution.

3. A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by other means of transport are respectively 3/10, 1/5, 1/10 and 2/5. The probabilities that he will be late are ¼, 1/3 and 1/12, if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he is late. What is the probability that he comes by train?

4. An entrance examination for admission to a first degree course in medicine was conducted at the national level. The mean and standard deviation of the marks obtained by 15000 candidates were 40 and 8, respectively. Determine in terms of standard deviation, the standard marks of students getting 50 and 60 marks. Also find the marks obtained corresponding to standard marks 1.30 and 1.50.

5. What is standard error of estimate? How is it measured? List some of its important interpretations.

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