Coursepack , p. 610 MAT 133 : ( FA22 ) Sample Midterm Exam, p. 12 3) The probability distribution below is for the average hours of sleep per night for Americans. Hours of Sleep Probability a) Explain what must be true in order to verify that 4 0.04 this is a valid probability distribution . 0.09 0.25 40 DO V G UT 0.3 (Circle one) 0.27 b) The given probabilities are Subjective 0.03 Classical Empirical 0.02 c) Compute the mean of the distribution: Hx= (2 decimal places ) d) Compute the standard deviation of the distribution: ox= (3 decimal places) e) Interpret the mean and standard deviation in the context of the situation. e) What is the probability that a random American sleeps from 7 to 9 hours, inclusive, per night? (Circle one) 0.25 0.27 f) To calculate part e), we must presume that values for "hours of sleep" are: (Circle one) 0.60 0.62 Disjoint Not Disjoint Independent Dependent g) The probability that a random American sleeps at least 6 hours a night is: (Circle one) 0.25 0.38 0.62 0.87 h) What is the probability that a random American does not sleep 8 hours per night? (Circle one) 0.27 0.73 0.32 0.68 i) If TWO random Americans were selected, the probability that both of them sleep an average of 8 hours a night is: (Circle one) 0.0729 0.135 0.27 0.54 j) To calculate part i), we must presume that the individuals selected are: (Circle one) Disjoint Not Disjoint Independent Dependent