Q1: Score or a certula atlon-wide college entrance examination follows bermal distribution with a mean of 400 and a standard deviation of 80. Find the probability that a student will scare D Less than 300 1) Greater than 500 HD) Between 325 and 385 polata) D Q2: Let X be a rundom variable with range (0, 1) and pdf f(x) = 3x?. Show that f(x) is a probability density function. ) Find P(X > . tih) Find cumulative distribution function (CDF). (4 points) Q 3: Let X be the random variable representing the sum of dots which appears on the dice. The probability density function of X is given as: P(x = x) = 6-17-21 x=2,3,4,..., 12. 36 1) Find the probability that a sum of dots is 8 or 11. ) Find the probability that a sum of dots is 13 or 14. Find the probability that a sum is less than 4. Iy) Find the probability that a sum is greater than 4 but less than equal to 6. (4 points) Q4: In a bolt factory, Machine A, B and C manufacture 25, 35, and 46 percent of the bolt output. Of their outputs $, 4, and 2 percent are defective bolts. A bolt is selected at random and found to be non-defective. What is the probability that bolt come from Machine C! (3 points) Q5: The HBO cable network took a survey of 400 subscribers to determine people's favourite show, the data are shown in the following table: Subscriber Male Female Games of Thrones 30 West World 50 Others 85 80 60 95 i) ib) What is the probability of an HBO subscriber customer being Male What is the probability of an HBO subscriber customer being Male' and prefer *West Word? What is the probability of an HBO subscriber customer being Female or preferring West Word Given that subscriber is female. What is the probability of preferring Games or Thrones (4 points) ly)