Explain the characteristics and applications of discrete probability distributions Use the data given below to answer the following question(s).
On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year. (Hint: Use Poisson distribution formula).
-What is the probability of 8 takers or less for Arts subjects in the coming year?
A) 0.00716
B) 0.01260
C) 0.03164
D) 0.04744

Question

Quizplus · Accepted Answer

The given information suggests that we can use the Poisson distribution formula to solve this problem. The Poisson distribution is a discrete probability distribution that can be used to model the number of events that occur in a fixed interval of time, given that the events occur at a constant rate and independently of each other.

The formula for Poisson distribution is: P(X = x) = (e^(-λ) * λ^x) / x!, where λ is the average number of events per interval, and x is the number of events we are interested in.

In this case, λ = 17 (since the average number of students who choose Arts subjects each year is 17). We are interested in the probability of 8 takers or less, so x can take the values from 0 to 8.

Using the formula, we can calculate the probabilities for each of these values of x and add them up to get the total probability of 8 takers or less:

P(X ≤ 8) = Σ P(X = x), for x = 0 to 8

= P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 8)

= (e^(-17) * 17^0) / 0! + (e^(-17) * 17^1) / 1! + (e^(-17) * 17^2) / 2! + ... + (e^(-17) * 17^8) / 8!

= 0.01260 (approx.)

Therefore, the answer is choice letter B.

Explain the Characteristics and Applications of Discrete Probability Distributions Use