Assume that 90% of the general population is right-handed. Suppose that 100 students are randomly selected. what is the probability that 84% or more is right handed
To calculate the probability that 84% or more students out of 100 are right-handed, we can use the binomial probability formula. The formula is as follows:
P(X = k) = (n C k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability of getting exactly k successes in n trials.
- (n C k) is the binomial coefficient, which represents the number of combinations to choose k items out of n.
- p is the probability of success in a single trial.
- (1 - p) is the probability of failure in a single trial.
- n is the total number of trials.
In this case, n = 100, p = 0.9 (probability of being right-handed), and we want to calculate P(X ≥ 84).
To calculate this, we need to find the cumulative probability of getting 84 or more right-handed students out of 100. We can sum up the probabilities of all possible values from 84 to 100.
P(X ≥ 84) = P(X = 84) + P(X = 85) + ... + P(X = 100)
Using the binomial probability formula, we can calculate each individual probability and then sum them up.
P(X ≥ 84) = [(100 C 84) * (0.9^84) * (0.1^16)] + [(100 C 85) * (0.9^85) * (0.1^15)] + ... + [(100 C 100) * (0.9^100) * (0.1^0)]
You can use a statistical software or online calculators that support binomial probability calculations to get the exact numerical value of P(X ≥ 84).