Question

ved at the post office is exponential meter 3 minutes. Use this information amount of time a customer waits to be served at - cation parameter 6 minutes and scale parameter 3 to answer questions 3 and 4. 3. What is the expected value and variance of customer exponentially distributed with is information and the next page of customer wait time? A+B (MEN) Ex) = -Al Blog12) Vor=p² 6/10 = 7 ml Juarcx) = q nomutes 4. To monitor customer wait times, a device is installed at the service window that asks 30 randomly selected customers how long they waited to be served every day. If the mean wait time for these customers is greater than 10 minutes, a notification is sent to headquarters. On what proportion or days will a notification be sent? n=30 760-61 USE C.C.T. 2 10/30 966

Can someone help me with these, I need help understanding.

Answer 1

Mat if Know We x follows vamable andom dishmibuhion e xponential Location paname her wirh scale parame Her and pdf of X e B, hen i s -1x-A)/P flu B >O 0.W.

and ElX) tB 2 Varlx)- B 3) denotes he X Let of time in amount minutes) customer be served at waits the post office i exponentially Here X dishmbute d with Loeation parameher 6 minutes and Seale minutes 3 parameter and 3

expected Wait Valne of The ime is customenr ElX)- + 6 3 minutes 9 of custo mer Vamance ime wait 2 Varlx)-B 2 2 9 (minutes) A) Let denotes Xi he f Hme wait he andamly Selected customer iI,2.. 30

3 0 X X 3 0 No he hat mean he denotes Oof mese ime wait customes Limit central Вy heoreml cLT) Know we ;f hat iI,2 n and sufficiently Large i.e. n 30 ) hen NELX) Varlx) whene 27

pmoblem, his In h n 30( 30 ElX) 9, He re Var Lx) 9 CLT By XNL 9 30 N , 3

notifieahion that No te he is sent if X 1o headqnartes Now, 0-9 > 0 3 PIZ 8257) Let Z hen Jo 3 z NIO,1 1 - PIZ I8257)

1- 8257) 2) is the cdf of NLo, 1). 09661 0 0339 . . A notification will be sent 0. 0339 On poportion ot days.