Final answer:
The probability of finding five left-handers in a class of 23 students is 0.064.
Step-by-step explanation:
To find the probability of finding five left-handers in a class of 23 students, we can use the binomial probability formula. The formula is:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
where P(X=k) is the probability of having exactly k successes, C(n,k) is the number of ways to choose k successes out of n trials, p is the probability of success, and n is the number of trials.
In this case, the probability of finding a left-hander is 0.19, so p = 0.19. We want to find the probability of finding exactly 5 left-handers, so k = 5. Since we have 23 students in total, n = 23. Plugging these values into the formula, we get:
P(X=5) = C(23,5) * 0.19^5 * (1-0.19)^(23-5) = 0.064