According to one study, 61% of the population swallow at least one spider per year in their sleep. Based on this study, what is the probability that exactly 7 of 10 randomly selected people have swallowed at least one spider in their sleep in the last year? (1 point) Responses 70% 70% 22% 22% 1% 1% 34%
22%
To calculate the probability, we can use the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where:
- n = number of trials (10 people)
- k = number of successes (7 people)
- p = probability of success (61% or 0.61)
Plugging in the values:
P(X=7) = (10 choose 7) * 0.61^7 * (1-0.61)^(10-7)
P(X=7) = (10! / (7!(10-7)!) ) * 0.61^7 * 0.39^3
P(X=7) = 120 * 0.061 * 0.029
P(X=7) = 0.20796
Therefore, the probability that exactly 7 out of 10 randomly selected people have swallowed a spider in their sleep in the last year is approximately 22%.