Question

58% of all Americans are home owners. Round your answers to four decimal places. If 45 Americans are randomly selected, find the probability that

a. Exactly 26 of them are are home owners.


b. At most 28 of them are are home owners .

c. At least 27 of them are home owners .

d. Between 25 and 29 ( including 25 and 29 ) of them are home owners .

Answer 1

To find the probability, use the binomial probability formula: P(X = k) = C(n, k) * p^k * (1 - p)^(n - k). Use the formula to find the probabilities in each case. Round the answers to four decimal places.

Step-by-step explanation:

To find the probability in each case, we will use the binomial probability formula:

a. Exactly 26 of them are homeowners:

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

P(X = 26) = C(45, 26) * (0.58)^26 * (1 - 0.58)^(45 - 26)

P(X = 26) = 0.1164

b. At most 28 of them are homeowners:

P(X ≤ k) = P(X = 0) + P(X = 1) + ... + P(X = k)

P(X ≤ 28) = P(X = 0) + P(X = 1) + ... + P(X = 28)

P(X ≤ 28) ≈ 0.8572

c. At least 27 of them are homeowners:

P(X ≥ k) = 1 - P(X < k)

P(X ≥ 27) = 1 - P(X < 27)

P(X ≥ 27) ≈ 0.5797

d. Between 25 and 29 (including 25 and 29) of them are homeowners:

P(25 ≤ X ≤ 29) = P(X = 25) + P(X = 26) + ... + P(X = 29)

P(25 ≤ X ≤ 29) ≈ 0.9131