Question

The Gallup organization found that 26% of Americans own a cat asa pet. Round all probabilities to four decimal places. a) Find theprobability that 4 Americans own a cat as a pet.

Answer 1

The probability that 4 Americans own a cat as a pet, with a 26% ownership rate, is found using the binomial probability formula. This results in a probability of 0.0046 when rounded to four decimal places.

Step-by-step explanation:

The question asks for the probability that 4 Americans own a cat as a pet, given that 26% of Americans own a cat. To find this probability, we can model the scenario with a binomial distribution since each American owning a cat can be considered an independent Bernoulli trial with two possible outcomes (either they own a cat or they do not).

The binomial probability formula is:

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

Where:

• n is the number of trials (Americans)
• k is the number of successes (cat owners)
• p is the probability of success on a single trial (26% or 0.26)

When n = 4 and k = 4:

P(X = 4) = (4 choose 4) * 0.26^4 * (1-0.26)^(4-4)

P(X = 4) = 1 * 0.26^4 * 1

P(X = 4) = 0.0046 (rounded to four decimal places)

Thus, the probability that all four Americans sampled own a cat as a pet is 0.0046.