According to one study, 61% of the population swallow at least one spider per year in their sleep.

Question

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)

70%

22%

1%

34%

Answer 1

This can be calculated using the binomial probability formula:

P(X=k) = nCk * p^k * (1-p)^(n-k)

where n = 10 (number of randomly selected people), k = 7, p = 0.61 (probability of swallowing at least one spider per year), and 1-p = 0.39

Plugging in the values:

P(X=7) = 10C7 * (0.61)^7 * (0.39)^3 = 120 * 0.061337 * 0.027729 = 0.2005

Therefore, the probability that exactly 7 of 10 randomly selected people have swallowed at least one spider in their sleep in the last year is 20.05%.

So the closest option to this answer would be 22%.