The number of hits to a website follows a Poisson process. Hits occur at the rate of 6.8 per minute between 7:00 P.M. and 11:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenariobetween 10:13 P.M. and 10:14 P.M. Interpret each result.(a) exactly seven(b) fewer than seven(c) at least seven.....(a) P(7) =(Round to four decimal places as needed.)On aboutof every 100 time intervals between 10:13 P.M. and 10:14 P.M, the website will receivehit(s).(Round to the nearest whole number as needed.)(b) P(x <7)=|(Round to four decimal places as needed.)On aboutof every 100 time intervals between 10:13 P.M. and 10:14 P.M, the website will receivehit(s).(Round to the nearest whole number as needed.)(c) P(x27) =(Round to four decimal places as needed.)On aboutof every 100 time intervals between 10:13 P.M. and 10:14 P.M, the website will receivehit(s).(Round to the nearest whole number as needed.)Time Remaining: 02:30:52NextDEC16étv280MacBook Air80QDIIDDescF1F2F3F4F5F6F7F8F9F10F11F12$1245678del{QWEтYP1R#3

It is given that the number of hits to a website follows Poisson process with average rate 6.8 per minute.(a) The Poisson probability distribution is, PX=x=e-λλxx!;x=0,1,2,.... In the distribution λ be the average. The probability that exactly seven occur between 10:13 P.M. and 10:14 P.M. is, PX=7=e-6.86.877!=0.1486 Thus, the probability that exactly seven occur between 10:13 P.M. and 10:14 P.M. is 0.1486. On about 15 of every 100 times intervals between 10:13 P.M. and 10:14 P.M., the website will receive exactly 7 hits.(b) The probability that fewer than seven occurs between 10:13 P.M. and 10:14 P.M. is, PX<7=PX=0+PX=1+PX=2+PX=3+PX=4+PX=5+PX=6=e-6.86.800!+e-6.86.811!+e-6.86.822!+e-6.86.833!+e-6.86.844!+e-6.86.855!+e-6.86.866!=0.0011+0.0076+0.0258+0.0584+0.0992+0.1349+0.1529=0.4799 Thus, the probability that fewer than seven occur between 10:13 P.M. and 10:14 P.M. is 0.4799. On about 48 of every 100 times intervals between 10:13 P.M. and 10:14 P.M., the website will receive fewer than 7 hits.(c) The probability that at least seven occurs between 10:13 P.M. and 10:14 P.M. is, PX≥7=1-PX<7=1-0.4799=0.5201 Thus, the probability that at least seven occur between 10:13 P.M. and 10:14 P.M. is 0.5201. On about 52 of every 100 times intervals between 10:13 P.M. and 10:14 P.M., the website will receive at least 7 hits.