Department of Physical Science MAT 211: Probability and Statistics (Section: 6) 2nd quiz Examination Spring-2023 Total Marks: 15 1 22 Instruction: Answer any three questions 1) The time needed to complete a final examination in MAT-121 course is normally distributed with mean of 100 minutes and variance 144 minutes. Answer the following questions. a) What is the probability that a student will complete the examination in less than 75 minutes? b) That is the probability that a student will complete the examination between 70 to 110 minutes? c) Assume that the class has 38 students and the examination period is 120 minutes in length. How many students do you expect will be unable to complete the examination in the allotted time? 2) The reaction time of a driver to visual stimulus is normally distributed with a mean of 0.4 seconds and a standard deviation of 0.05 seconds. a) What is the probability that a reaction requires more than 0.5 seconds? b) What is the probability that a reaction requires between 0.4 and 0.5 seconds? c) What is the reaction time that is lower 5% of the time? 3) In a statistical investigation, the grade point average and study hour of a group of the following IUB students in one semester are recorded as follows Grade point average: 3.8, 3.5, 4.0, 2.5, 2.0, 4.0 Study hour : 15, 14, 16, 17, 14, 15 a) Which one is dependent variable? Fit a regression model and make summary based on your model. b) Predict the grade point average of a student if He or She works for 18 hours. 4) The data shown in the following table are highway gasoline mileage performance (Y) and engine displacement (X) for a sample of 6 cars Brand 1 22 BMW Chevrolet Dodge Ford Mercedes MPG (Highway) 19 32 28 25 24 Nissan 26 Engine Displacement (in) 209 121 181 302 159 181 4 1 S a) Develop a scatter diagram. What does this scatter diagram indicate about the relationship between the two variables? b) Determine the sample correlation coefficient between these two variables and write down a comment on your results.