Assume that X has the distribution N (10, 4), find:   P (Z > - 3)     P (11.36 < X < 16)

Eighteen individuals are scheduled to take a driving test at a particularDMV office on a certain day, eight of whom will be taking the test for thefirst time. Suppose that six of these individuals are randomly assigned toa particular examiner, and let Xbe the number among the six who aretaking the test for the first time. a. What kind of a distribution does Xhave (name and values of allparameters)?b. Compute P(X = 2), P(X ≤ 2), and P(X≥2).c. Calculate the mean value and standard deviation of X.

Let � be a continuous random variable distributed by �(11,1.2), find:A) �(�≥8.89)=  Keep your answer in 4 decimal places.B) �(�>11.97)=  Keep your answer in 4 decimal places.**Notes: DO NOT round any z-score.

Suppose the random variable X has a continuous uniform distribution on the interval (20,80).  What is P(X > 52 | X > 28)? (Give your response to at least 3 decimal places

Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value  has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of  x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.

D5) X and Y are two points that are selected according to a uniform distribution. Calculate the expected value of the distance between these two points for each of the following cases: a) Both X and Y are selected independently from the range 0-1. b) We select X between 0 and 1 and then select Y between 0 and X. Note: For case b the distance is equal to |Y-X|