Answer:
a) 0.4481
b) 0.1298
c) 0.6722
Explanation:
English Translation
It is known that 20% of all people given a certain medicine feel very bad in 2 minutes; Find the probability that among 14 people who are given this medicine:
a) At most 2 feel very bad in two minutes
b) At least 5 feel very bad in two minutes
c) From 2 to 4 they feel very bad in two minutes
Solution
This is a binomial distribution problem
A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.
It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure.
The outcome of each trial/run of a binomial experiment is independent of one another.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 14
x = Number of successes required
p = probability of success = probability of feeling bad after taking the medicine = 20% = 0.20
q = probability of failure = probability of NOT feeling bad after taking the medicine = 1 - 0.20 = 0.80
a) At most 2 feel very bad in two minutes
P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)
= 0.04398046511 + 0.15393162789 + 0.25013889532 = 0.44805098832 = 0.4481
b) At least 5 feel very bad in two minutes
P(X ≥ 5) = 1 - P(X < 5) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)]
= 1 - [0.04398046511 + 0.15393162789 + 0.25013889532 + 0.25013889532 + 0.17197049053] = 0.12983962583 = 0.1298
c) From 2 to 4 they feel very bad in two minutes
P(2 ≤ X ≤ 4) = P(X=2) + P(X=3) + P(X=4)
= 0.25013889532 + 0.25013889532 + 0.17197049053 = 0.6722482811 = 0.6722
Hope this Helps!!!