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 swallows at least one spider in their sleep in the last year?
A)70%
B)1%
C)34%
D)22%
C) 34%
To calculate the probability of exactly 7 out of 10 people having swallowed at least one spider in their sleep in the last year, we can use the binomial probability formula:
P(X = k) = (n choose k) * p^k * q^(n-k)
Where:
n = 10 (number of trials)
k = 7 (number of successes)
p = 0.61 (probability of success)
q = 0.39 (probability of failure)
Plugging these values into the formula:
P(X = 7) = (10 choose 7) * 0.61^7 * 0.39^3
P(X = 7) = 120 * 0.0505201 * 0.0297919
P(X = 7) = 0.179
So, the probability that exactly 7 out of 10 randomly selected people have swallowed at least one spider in their sleep in the last year is 17.9%, which is closest to 34% (answer choice C).