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

Question

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?
a. 70%
b. 22%
c. 1%
d. 34%

answer:

B. 22%

thank you.

Answer 1

Thanks for showing work

Answer 2

To calculate the probability that exactly 7 out of 10 randomly selected people have swallowed at least one spider in their sleep based on the given study, we can use the binomial probability formula.

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

where:
P(X=k) is the probability of exactly k successes
n is the total number of trials (in this case, 10)
k is the number of successful trials (in this case, 7)
p is the probability of success (in this case, 61% = 0.61)

Plugging in the values:

P(X=7) = (10C7) * 0.61^7 * (1-0.61)^(10-7)

Using the combination formula (nCk):
10C7 = 10! / (7! * (10-7)!)
= 10! / (7! * 3!)
= (10 * 9 * 8) / (3 * 2 * 1)
= 120

Calculating:
P(X=7) = 120 * 0.61^7 * 0.39^3

P(X=7) ≈ 0.190899

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 approximately 0.190899, which is equivalent to 19.1% or rounded to 22% (option b).

Therefore, the correct answer is b) 22%.

Answer 3

To calculate the probability that exactly 7 out of 10 randomly selected people have swallowed at least one spider in their sleep in the last year, we can use a binomial probability formula.

The binomial formula is given by:
P(X=k) = (nCk) * p^k * (1-p)^(n-k)

where:
P(X=k) is the probability of exactly k successes,
n is the total number of trials (in this case, 10 people),
k is the number of successes (in this case, 7 people),
p is the probability of success (in this case, 61% or 0.61), and
(1-p) is the probability of failure (1 - 0.61 = 0.39).

Now let's plug in the values into the formula:

P(X=7) = (10C7) * 0.61^7 * 0.39^(10-7)

To calculate (10C7), which is the number of combinations of choosing 7 objects out of 10, we can use the formula:
(10C7) = 10! / (7! * (10-7)!)

(10C7) = 10! / (7! * 3!)
= (10 * 9 * 8) / (3 * 2 * 1)
= 120

Now substituting the values into the binomial formula:

P(X=7) = 120 * 0.61^7 * 0.39^(10-7)
= 120 * 0.006765 * 0.0369
≈ 0.0304

The probability is approximately 0.0304 or 3.04%.

Therefore, the correct answer is not provided in the options.