Question

A community centre is going to hold a yaga class with 15 regisitered students. From the previous report of Yoga class, the absent rate per students is 5%. i) Calculate the probability that at most 13 students will attend the yoga class.

Answer 1

Solution :

Let X be a random variable which represents the number of students who will present for yoga class in 15 registered students.

Given that, absent rate is 5%. Hence, present rate is 95%. Hence, the probability that a student will present for the yoga class is 95/100 = 0.95.

Let us consider "a student who will present for yoga class" as success. Hence, we have now only two mutually exclusive outcomes.

Probability of success (p) = 0.95

Number of trials (n) = 15

Since, probability of success remains constant in each of the trials, number of trials are finite, we have only two mutually exclusive outcomes for each of the trials and outcomes are independent, therefore we can consider that X follows binomial distribution.

According to binomial probability law, probability of occurrence of exactly x successes in n trials is given by,

Where, p is probability of success.

We have to obtain P(X = at most 13).

We have, p = 0.95 and n = 15

P(X = at most 13) = P(X ≤ 13).

P(X ≤ 13) = 1 - P(X > 13)

P(X ≤ 13) = 1 - [P(X = 14) + P(X = 15)]

Using binomial probability law we get,

Hence, P(X = at most 13) = 0.1709

The probability that at most 13 students will attend the yoga class is 0.1709.

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