Question

68. Eighteen individuals are scheduled to take a driving test at a particular DMV dice on a certain day, eight of whom will be taking the test for the first time. Suppose that six of these individuals are randomly assigned to a particular examiner, and let X be the number among the six who are taking the test for the first time. a. What kind of a distribution does X have (name and values of all parameters)? 2), and P(X> 2). b. Compute P(X 2), P(X c. Calculate the mean value and standard deviation of X.

Answer 1

Sotution- Guim that af imdiuiduals N18 The Yumbur the fryt tme forh tust Thu 8=W Sampl Su be obsaurd infarmation Hhe Can Fhom 9uen that foleus the nandom Uariahle distribution with Patam us N18, m 8, amd n- b. That i, X Hypanguom (N18, r , n) b Compute p(x =1), P(x2), and P(x22) the valu ot P(1 2) Find Fhom Part (a), tu phobabiliby density pundion, of the hauguomebui disthibution N-M M n-x Plx)

18 -8 6 に2)G) ,X 0, 1-8 umber of thu s Sampu the Suze m is Sulurs the nlumber of tailurs N-M Now, Calulati P(x-2). P(-2) 2 18 (210) 28 18554 0.316 7 Tharfore, the valut of P(x - 2) O.3167 0.3167

the Valu P(x2) Find >Plxel)=P(x-o)+ P(x)P(x -2) 8 18 -8 8-81 6-0 81 6 -2 6-1 + 18 0.0113 + 0.1086 + 0. 3167 O.4366 1hurferde, thu valu t P(x2) 0.u366 Find Plx21) the Ualu Pl) 1- P(12) 1-P(-o) P(x- G 18-9 8 81 6-O 8 6-1 18 1- f0.0u34 010 36 088.0 Thertforre, the value P(x21) 0-880

diviation of the handom Vahable Standand amd The Tmeam foloung foh mula The the mtan (s) 9 18 2.67 Thiraforre Hhe mean 2 67 Thu Standahd duration uing the tollouimg formula N-n N N-1 18-6 (2.67) - 18 18-1 -1 1-O471 I.O233 handom Thurafare dination Stamdaid thu Jariable 10233