Question

4-87. Hits to a high-volume Web site are assumed to follow a Poisson distribution with a mean of 10,000 per day. Approxi- mate each of the following: (a) Probability of more than 20,000 hits in a day (b) Probability of less than 9800 hits in a day (c) Value such that the probability that the number of hits in a day exceeds the value is 0.01 (d) Expected number of days in a year (365 days) that exceed 10.200 hits. (e) Probability that over a year (365 days), each of the more than 15 days has more than 10.200 hits. 4-88. Anne

Answer 1

Solut fon: iven peisson distoi bion .wIth a Mean ob t0,00o perday а) Cwe need fo del enine +he poba btr thosp MO. Hhan 2000o hits In a day day In a vey lange thot huriben ot hlts p C ppse xiotian ot the poisson olih Jhen cESe NoaHa CoDse cHOn Conttnuity using continuity Cosectin P/x >20000) FP(x£ 2 00O0.5) 20000-5 20000 S10000 VA P(2 (00-oo5) P(X20000) 0.0000 dn this ae need to determine the pyobabiliiy a b th at less than qs0ohits in a day th Jhat ob hits pen day is veny lange ob hu Mben ok-.the poi $on appоxiмсion Then NoxMaf USe

wIth continvity coosec lion P(A 9800) = P(X< 9800 - 0-S) 9799.S0 -A VA 9799.50-(000 P/2 Vioc0o P(X9800) -OO22-2 n dhs we need to defenMine the vdie o6Such thort the Pso babl 11ty 1s the norbel o t hits In a pen duy Ekceeds to the value In this noMben ot- hits pen cky sveny longer they a ppso yiHtfon o6 the pois so h the ob NoMal cese wtA Continal ty Cosectloh PCX 001 PCXto-5)=0 0) t050-A 1- P Lz3)O 01

>) these st an dand nosHa abfe 1svo LEs ob the obseve that he cH volue 1s o the one tot est 4hd the sponding oE the WMulotive aneuls of Snce Z 2.3 3 0-5- 2-33 t0.S2-33 VA +A 233 (V000 6 t0.50-10000 = 10000 t2.33(l09 = (0000 t233 I0233 o-50 02.2-2.S X - T02.2.2 5 02-33 l0223