Question

4. a random sample of 2400 people are asked if they favor a government proposal to develop new nuclear power plants. if 40 percent of the people in the country are in favor of this proposal, find the expected value and the standard deviation for the number of people in the sample who favored the proposal.

Answer 1

The standard deviation for the number of people in the sample who favor the proposal is 24.

Explanation:

In this scenario, we can model the number of people who favor the proposal in the sample as a binomial random variable because each person in the sample either favors the proposal (success) or does not favor the proposal (failure), with a fixed probability of success for each person.

For a binomial random variable, the expected value (mean) and standard deviation are calculated as follows:

- The expected value (mean) \( \mu \) is given by \( \mu = n \cdot p \), where \( n \) is the number of trials (sample size) and \( p \) is the probability of success on each trial.

- The standard deviation α is given by
`√(n.p. (1-p))`

Given:

- The sample size
`n = 2400` people.

- The probability of a person favoring the proposal
`p = 0.40` (40 percent).

Let's calculate the expected value and the standard deviation.

The expected value for the number of people in the sample who favor the proposal is 960.

The standard deviation for the number of people in the sample who favor the proposal is 24.

Answer 2

The standard deviation for the number of people in the sample who favor the proposal is 24.

In this scenario, we can model the number of people who favor the proposal in the sample as a binomial random variable because each person in the sample either favors the proposal (success) or does not favor the proposal (failure), with a fixed probability of success for each person.

For a binomial random variable, the expected value (mean) and standard deviation are calculated as follows:

- The expected value (mean) \( \mu \) is given by \( \mu = n \cdot p \), where \( n \) is the number of trials (sample size) and \( p \) is the probability of success on each trial.

- The standard deviation
`\( \sigma \)` is given by
`\( \sigma = √(n \cdot p \cdot (1 - p)) \)`.

Given:

- The sample size
`\( n = 2400 \)` people.

- The probability of a person favoring the proposal
`\( p = 0.40 \)` (40 percent).

Let's calculate the expected value and the standard deviation.

The expected value for the number of people in the sample who favor the proposal is 960.

The standard deviation for the number of people in the sample who favor the proposal is 24.