During a meteor shower, 'shooting stars' occur at an average rate of 12 per minute or .2 per second.Assume all the Poisson conditions are met.What is the probability of between one and three 'shooting stars' in a 20-second time interval?
A).4152
B).2587
C).3216
D).3762
E).4585

Question

Quizplus · Accepted Answer

The probability of between one and three 'shooting stars' in a 20-second time interval is the sum of the probabilities of one, two, and three 'shooting stars' in a 20-second time interval. The probability of one 'shooting star' in a 20-second time interval is given by the Poisson distribution as:P(X = 1) = (e^-4) * 4 / 1! = 0.2587The probability of two 'shooting stars' in a 20-second time interval is given by the Poisson distribution as:P(X = 2) = (e^-4) * 4^2 / 2! = 0.1552The probability of three 'shooting stars' in a 20-second time interval is given by the Poisson distribution as:P(X = 3) = (e^-4) * 4^3 / 3! = 0.0517Therefore, the probability of between one and three 'shooting stars' in a 20-second time interval is:P(1 <= X <= 3) = P(X = 1) + P(X = 2) + P(X = 3) = 0.2587 + 0.1552 + 0.0517 = 0.4152

During a Meteor Shower, 'Shooting Stars' Occur at an Average