Answer Happy

Fyan and Miriam are roommates who take the bus 396 together almost every weekday to go to Down-Under university. Let X be their waiting time at the bus stop (in minutes) before the bus 396 arrives. The random variable X follows a Bus396 distribution with mean 9.1 and standard deviation 2.8, whose density function roughly looks like: Let X1​ be their waiting time the first time they take the bus 396 , let X2​ be their waiting time the second time they take the bus 396, etc. The waiting times at the bus stop are independent. During a term at Down-Under university, Ryan and Miriam take that bus together 89 times. Ryan and Miriam's average waiting time at the bus stop during the term is Xˉ=89X1​+X2​+X3​+⋯+X89​​
c) What is the mean of Xˉ ? (Enter the exact value in the box bolow.) d) Calculate the standard deviation of Xˉ. [4 (Enter the numerical part of your answer corroct to at least 4 decimal places in the box below. 2) Dr Tatauranga, Ryan and Miriam's lectuyer at Down-Under university, points out that if you add their 89 waiting times at the bus stops during a term, you will see that Ryan and Miriam spend hours and hours waiting at the bus stop over a term! Using the approximation mentioned in question 1), what is the probability that Ryan's total waiting time at the bus stop over the course of a term will exceed 13 hours? (En)er the numerical part of your answer correct to at least 3 significant figures in the box below.)