Question

A company is preparing to launch a new web site to sell its products. From past experience, they know that purchases at the site will occur as a Poisson process with on average 30 purchases every 10 minutes.
a) What is the expected time in minutes before the first purchase after the site opens? Give your answer to four decimal places. ANS: 0.3333 (correct)
b) What is the probability that more than 0.14 minutes pass before the first purchase? Give your answer to four decimal places. ANS: 0.6570 (correct)
c) What is the expected time in minutes until the fifth purchase? Give your answer to four decimal places. ANS: 1.6667 (correct)
d) What is the probability that the eighth purchase will occur between 1.33 minutes and 2 minutes after the site opens? Give your answer to four decimal places. (NEED HELP)

Answer 1

Answer:

a. 0.333

b. 0.657

c. 1.667

d. -4.07

Step-by-step explanation:

a. Expected time of the first purchase is 10/30 = 0.333

b. Probability for time of 0.14 minutes before first purchase is :

e^-rt, r = 30/10 = 3 , t = 0.14

e^ -3 * 0.14 = 0.65704

c. Expected time until 5th order :

1 / [30/10] * 5 = 1.6667

d. Probability that 8th purchase will occur between 1.33 and 2 minutes ;

[30/10 ] / [ 1/2] = 6

Chi squared distribution ;

1.33 * 6 - 2 * 6 = -4.02