Question

A financial services company is looking to study the types of investments participants make within their online platform. If 56% of the population allocates a quarter of their investments in real estate and the company randomly samples 45 participants, what is the probability that more than half of them have a quarter of their investments in real estate?

a) 0.795
b) 0.610
c) 0.205
d) 0.390

Answer 1

To find the probability that more than half of the sampled participants have a quarter of their investments in real estate, we calculate the probability of having 23 or fewer participants out of 45 with a quarter of their investments in real estate using the binomial probability formula. The probability is approximately 0.2046, so the probability that more than half have a quarter of their investments in real estate is 0.7954.

Step-by-step explanation:

To find the probability that more than half of the randomly sampled participants have a quarter of their investments in real estate, we need to calculate the probability of having 23 or fewer participants out of 45 with a quarter of their investments in real estate.

We can use the binomial probability formula P(X ≤ k) = C(n, k) * p^k * q^(n-k), where n is the sample size, k is the number of successful outcomes, p is the probability of success, and q is the probability of failure.

In this case, n = 45, k ranges from 0 to 23, p = 0.56, and q = 1 - p = 0.44.

Using this formula, we can calculate the probability and find that the probability of having 23 or fewer participants out of 45 with a quarter of their investments in real estate is approximately 0.2046. Therefore, the probability that more than half of the sampled participants have a quarter of their investments in real estate is 1 - 0.2046 = 0.7954. So, the answer is option a) 0.795.