suppose that a population of people is 1200. .25 of the population is white. we take a random sample of 100 people. What is the probabilit that more than .29 of these people are white?

To find the probability that more than 0.29 of the people in the random sample are white, we need to use the concept of probability distribution and the binomial distribution in this case.

Let's break down the problem:

1. Determine the population size: The population size is given as 1200 people.

2. Calculate the number of white people in the population: Since 0.25 of the population is white, we can calculate the number of white people as 0.25 * 1200 = 300.

3. Define the number of white people in a random sample: Let's denote the number of white people in a random sample of 100 people as X.

4. Determine the sample distribution: Since the sample size is large (100), the distribution can be approximated by the normal distribution due to the Central Limit Theorem. We need to calculate the mean (μ) and standard deviation (σ) of the distribution.

μ = n * p = 100 * 0.25 = 25
σ = sqrt(n * p * (1 - p)) = sqrt(100 * 0.25 * 0.75) = sqrt(18.75) ≈ 4.33

5. Calculate the probability: To find the probability that more than 0.29 (or 29%) of people in the random sample are white, we need to calculate the probability that X is greater than 29.

P(X > 29) = 1 - P(X ≤ 29) = 1 - Φ((29 - μ) / σ)

Where Φ represents the cumulative distribution function (CDF) of the standard normal distribution. We can use a statistical table or a calculator to find the probability associated with the z-score ((29 - μ) / σ).

So, to find the probability, you can use a standard normal distribution table or a statistical calculator to find the probability associated with the calculated z-score.