Due to the health crisis, only 70 dorm students wish to go to campus every morning: 40 early birds, each arriving at the shuttle stop at a uniform continuous time between 9:00 and 9:15, and 30 late risers, each arriving at the shuttle stop at a uniform continuous time between 9:15 and 9:30. Correspondingly, just two shuttles run each morning, one departs the dorm at 9:10, 9:12, and 9:15 with probabilities 0.3, 0.5, and 0.2, respectively, and the other departs exactly fifteen minutes after the first: 9:25 if the first left at 9:10, and similarly 9:27, and 9:30. Each shuttle takes all students present when it departs, hence in particular, all early birds make it to school. Student arrival times are independent of each other and of the shuttle departure times. Let X and Y respectively be the random number of students taking the first and second shuttles on a given day. (a) Find E(X). (b) Find E(Y). (c) Use Chebyshev's Inequality to upper bound P(X > 35). (d) Use the Chernoff bound to upper bound P(X Y

x+y = 29, 5x + 2y = 100

step-by-step explanation:

i'm guessing it was a multiple first option was the correct answer

5 x 14?

im new, sorry if this is wrong.

step-by-step explanation:

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.