kercise 3.4.7. (Repeated from Lecture 3.4). Let RE, ="Nature generates a party attendee." The number f hamburgers eaten (X) has a probability distribution [wrt RE,] characterized by P(X = 0) = 0.5, (X = 1) = 0.4, P(X = 2) = 0.1. %3D a) What is the mean of X, mean(X:RE,)? b) What is the standard deviation of X, sd(X:RE,)? c) If 500 people will attend the party (i.e. RE,(500) will be carried out), what are the chances that they will eat more than 350 hamburgers? d) If 500 people will attend the party (i.e. RE,(500) will be carried out), how many hamburgers should be ordered so that there is only a 5% chance of running short?

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Question 30 A randomly selected realtor's monthly commission (in thousands) can be estimated by a random variable that follows F-distribution with parameters (14,4). Let X be the monthly commission of a randomly selected realtor. 1. Describe the distribution of X: (dfn= 14 2. Use the random variable notation to express symbolically each of the following: P(X<7.9) The probability of an event in which the monthly commission (in thousands) of a randomly selected realtor is less than 7.9. X-F X<7.1 An event in which the monthly commission (in thousands) of a randomly selected realtor is less than 7.1. P(X<13.1)=0.99 The probability of an event in which the monthly commission (in thousands) of a randomly selected realtor is less than 13.1 is equal to 0.99. ii. more than 7.9: 3. Use technology to find the probability that the monthly commission (in thousands) of a randomly selected realtor is: i. less than 7.1: iii. between 0.4 and 8: iv. more than 72.4: v. less than 98.3: 4. Find the 11-th…