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2. Answer the following questions based on probability distributions. [10 marks] a. Two assignments must be performed by the same employee. Assume: X = minutes to complete assignment 1; J. =20, ox = 5 Y = minutes to complete assignment 2; My =30, Gy = 8 If X and Y are normally distributed and independent, what is the mean and standard deviation of the time to complete both assignments? b. It is believed that the probability that an employee is absent on a particular day is 0.03. Assuming that there are 6 people in the office, what is the probability that at least one employee is absent tomorrow? c. If A and B are independent events with P(4) = 0.2 and P(B)=0.6, what is the value of P(A BY? d. The number of people entering a bank follows a Poisson distribution with an average of 5 arrivals/hour. What is the probability that at most seven people enter the bank in an hour? e. In a survey of 300 individuals, 62% indicated that they had been to a cinema within the past week. 75% of those individuals who had been to a cinema also had gone out to dinner in the past week, while only 64% of the individuals who had not been to a cinema had been out to dinner in the past week. Define the random variables as follows: X=1 if a person had been to cinema; X=0 otherwise; Y= 1 if a person had been out to dinner; )=0 otherwise. Find and interpret the covariance between Xand Y