Question

According to a 2019 eMarketer poll, 90.4% of individuals born between 1981 and 1996 (millennials) are active users of social media. Compute the following probabilities out of a group of 55 millennials. (Round your answers to three decimal places.)

(a) Find the probability that more than 48 are active on social media.

(b) Find the probability that at most 45 are active on social media.

(c) Find the probability that between 42 and 47 (including 42 and 47) are active on social media.

(d) Find the probability that exactly 48 are active on social media.

Answer 1

To solve this problem, we will use the binomial probability formula. (a) Find the probability that more than 48 are active on social media. (b) Find the probability that at most 45 are active on social media. (c) Find the probability that between 42 and 47 (including 42 and 47) are active on social media. (d) Find the probability that exactly 48 are active on social media.

Step-by-step explanation:

To solve this problem, we will use the binomial probability formula:

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

where n is the number of trials, k is the number of successes, p is the probability of success, and (nCk) is the number of combinations of n items taken k at a time.

a) To find the probability that more than 48 are active on social media:

P(X > 48) = 1 - P(X ≤ 48)

Substituting the values into the formula:

P(X > 48) = 1 - P(X ≤ 48) = 1 - Σ (nCk) * p^k * (1-p)^(n-k), where k ranges from 0 to 48.

b) To find the probability that at most 45 are active on social media:

P(X ≤ 45) = Σ (nCk) * p^k * (1-p)^(n-k), where k ranges from 0 to 45.

c) To find the probability that between 42 and 47 (including 42 and 47) are active on social media:

P(42 ≤ X ≤ 47) = Σ (nCk) * p^k * (1-p)^(n-k), where k ranges from 42 to 47.

d) To find the probability that exactly 48 are active on social media:

P(X = 48) = (nCk) * p^k * (1-p)^(n-k), where k is 48.