The random variable x is the number of occurrences of an event over an interval of ten minutes.It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length.It is known that the mean number of occurrences in ten minutes is 5.3.The probability that there are 8 occurrences in ten minutes is

A) .0241.
B) .0771.
C) .1126.
D) .9107.

Question

Gabby Mayhew · Accepted Answer

Final Answer : B, Explanation :  This problem can be modeled by a Poisson distribution, where the mean of the distribution is given as λ = 5.3. The probability of observing exactly k occurrences in a given interval is given by the formula P(X = k) = (e^-λ * λ^k) / k!, where e is the mathematical constant approximately equal to 2.718. Thus, the probability of observing exactly 8 occurrences in ten minutes is P(X = 8) = (e^-5.3 * 5.3^8) / 8! = 0.0771 (rounded to four decimal places). Therefore, the best choice is B.

Definitions

Learning Objectives

Learning Objectives

Related questions