Question

Suppose it will arrive at a total of 123 cars to a rock concert. From experience you know that
The probability that two people travel in a car is 25%. The probability of three people traveling in
a car is 50% and the probability of four people traveling in a car is 25%. About how big is
the likelihood that at least 385 car-borne spectators saw the concert?

Answer 1

Solation:ket X; denate he f people in ith car. aro futul /23 cars Then Thene C>l,2, 3,-, 2 3. The pmf of Xeん ir1,2,-g123 4 Ttal O 5 0L5 (2r0254 5* 3y0-51r025 ElX)=3 i21,2,-123. ZPm-) = (2'io25+3r05,42025) El= L+ E(X) New, 2+9+8 2 Vont.) Ex)E)= ( !12 _ 3°), 19-18 2 う/ Von 1X:) = The standerid Devistton of S0)= Va il,2123 Car-banne pecta tors sau the concont is, 12-3 X= X The fatal naof Then, Ex)ZEx)123x3 = 329. EIX)- 329

New Van(x)Vn(Ke) 23 avt XX;)=0 itj due to indopendones Var(x) 123x Van (x)= 615 Central Limit Thaorem (CLT)' sing X E(x) Van1X) Than Probabiity that the at Leaot 385-Car-bartna A pectatars saw the P(X389)- P( 35-) ert is eon P(X-329 P(X596) - P( 777.1408 Am Suweas Tha likeli hood that at leaot 395 aar-borne cont the con caw Apec tators