Probability_SamplePaper.pdf

JG UNIVERSITY DEPARTMENT OF CS & IT Sample Paper Mid-Term EXAMINATIONS,2023-24 BTech SEMESTER – II...

JG UNIVERSITY DEPARTMENT OF CS & IT Sample Paper Mid-Term EXAMINATIONS,2023-24 BTech SEMESTER – II Subject: Probability and Statistics Total Marks: 40 Duration: 1 hr ================================================================ Instructions: Attempt all questions. Make suitable assumptions wherever necessary. Figures to the right indicate full marks. Section – A {Multiple Choice Question [1x10 = 10 Marks]}: Q1. What is the arithmetic mean of the data set: 4, 8, 6, 10, 12? A. 7 B. 8 C. 9 D. 10 Q2. Which measure of central tendency is most appropriate when dealing with skewed data? A. Mean B. Median C. Mode D. Geometric Mean Q3. The harmonic mean is useful in calculating: A. Average of rates B. Central position C. Range of values D. Dispersion Q4. The quartile deviation is a measure of: A. Central tendency B. Dispersion C. Skewness D. Kurtosis Q5. In probability theory, two events are independent if: A. Their intersection is empty B. The occurrence of one event affects the occurrence of the other C. The occurrence of one event does not affect the occurrence of the other D. Both events are mutually exclusive Q6. The mean of five numbers is 14. Four of the numbers are 10, 18, 12, and 16. What is the fifth number? A. 14 B. 12 C. 18 D. 20 Q7. If the median of a data set is 25 and the sum of all observations is 300, how many observations are there? A. 10 B. 12 C. 15 D. 20 Q8. In a class of 20 students, 12 students study Mathematics, and 15 students study English. If 5 students study both subjects, how many students study neither? A. 2 B. 3 C. 5 D. 8 Q9. What is the combined standard deviation of two data sets: one with a standard deviation of 6 and the other with a standard deviation of 8, given that the total number of observations is the same for both data sets? A. 7 B. 7.5 C. 8 D. 10 Q10. In a symmetric distribution, the relationship between mean, median, and mode is: A. Mean = Mode > Median B. Mode > Mean = Median C. Mean = Median = Mode D. Mode < Median < Mean Section – B: Q11. In a probability experiment, you have a bag containing 5 red balls, 3 blue balls, and 2 green balls. a) If two balls are drawn sequentially without replacement, what is the probability that the first ball is red and the second ball is either blue or green? b) Calculate the probability that at least one of the two balls drawn sequentially without replacement is red. c) If three balls are drawn sequentially without replacement, what is the probability that exactly two of them are red and one is blue? [10 Marks] Q12. we have the following data -4,-2,0,-2,6,4,6,0,-6,4 Calculate the range, variance, and standard deviation of the data. [5Marks] Q13. Marks of the students in a particular subject of a class are given below. Find its variance and standard deviation. [5 Marks] Q14. A company conducted a survey to assess the productivity levels (in units produced per hour) of its employees. The survey results are grouped into the following frequency distribution table: The company wants to analyze the productivity data to make strategic decisions. For this, you need to: a) Calculate the exact mean productivity using the midpoints of the class intervals, and find the mean deviation from the mean. b) Determine the median productivity by calculating the median class interval and then compute the exact median productivity value. c) Find the modal class and calculate the exact mode of the productivity data, considering that the class intervals are of equal width. d) Calculate the coefficient of variation of the productivity data, given that the variance has been computed to be 100 (units/hour)^2. e) If the productivity data is altered by adding a new class interval with a frequency of 5 and a productivity range of 80 - 90 units/hour, re-calculate the mean and the median of the updated data. Assume the new class interval has a width of 10 units/hour and all other frequencies and intervals remain unchanged. [10 Marks] *************