Question

The number of hits to a website follows a Poisson process. Hits occur at the rate of 2.1 per minute 2.1 per minute between​ 7:00 P.M. and 11​:00PM. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 10:44 P.M. and 10:50 P.M. Interpret each result.

​(a) exactly six

​(b) fewer than six

(c) at least six

(a) P(6)= _____

On about _____of every 100 time intervals between 10:44 P.M. and 10:50 P.M, the website will receive_____ ,

______ hit(s).

(b)P(x<6)=_____

(round to four decimals as needed)

On about____ of every 100 time intervals between 100 time intervals between 10:44 PM and 10:50PM, the website will receive_______ ______hit(s).

(round to four decimals as needed)

(b) P(x≥6)= ______

(round to four decimal places as needed)

On about ____of every 100 time intervals between 10:44 PM and 10:50 PM, the website will _______ ____ hit(s).

(c) P(x≥6)= ______

(round to four decimal places as needed)

On about _____of every 100 time intervals between 10:44PM and 10:50PM, the website will receive_____ __(s).

(round to the nearest whole number as needed)

​

​

Answer 1

Time difference between 10:44 PM to 10:50 PM = 6 minutes.

Hit occur at the rate of 2.1 per minute.

Therefore for 6 minutes the rate is 6*2.1 = 12.6.

On about 2 of every 100 time intervals between 10:44 pm and 10:50 pm , the website will receive 6 hits

On about 1 of every 100 time intervals between 10:44 pm and 10:50 pm , the website will receive fewer than 6 hits

On about 99 of every 100 time intervals between 10:44 pm and 10:50 pm , the website will receive atleast 6 hits