Question

40% of the people in a state rent the home they live in. 1580 people are randomly selected. Let X be the number of people who rent the home they live in. What normal distribution best approximates X?

Answer 1

The number of people who rent their homes follows a normal distribution with a mean of 632 and a standard deviation of 19.89.

Step-by-step explanation:

The random variable X, which represents the number of people who rent the home they live in, follows a normal distribution.

In this case, since 40% of the people in the state rent their homes, the mean of the distribution (μ) is 0.4 multiplied by the total number of people randomly selected (1580), which is 632 people.

The standard deviation (σ) can be calculated by taking the square root of the product of the mean and the complement of the mean (1 - mean) multiplied by the total number of people.

Hence, σ = sqrt(0.4 * 0.6 * 1580) ≈ 19.89.