Reincarnation Suppose 21% of all American teens (age 13–17 years) believe in reincarnation.


d. In a survey of 100 American teens, how many would you expect to believe in reincarnation?

Verified step by step guidance

1. Identify the probability that a single American teen believes in reincarnation, which is given as 21%, or 0.21 in decimal form.
2. Recognize that the problem involves a sample of 100 American teens, so the total number of trials (n) is 100.
3. To find the expected number of teens who believe in reincarnation, use the formula for the expected value of a binomial distribution: \(E = n \times p\) where \(n\) is the number of trials and \(p\) is the probability of success.
4. Substitute the known values into the formula: \(E = 100 \times 0.21\).
5. Interpret the result as the expected number of teens out of 100 who believe in reincarnation.

Key Concepts

Probability and Proportion

Probability represents the likelihood of an event occurring, often expressed as a percentage or decimal. In this context, 21% means that out of all American teens, 21 out of 100 are expected to believe in reincarnation. Understanding this helps estimate expected counts in samples.

Expected Value

The expected value is the average outcome you anticipate from a random process over many trials. For a survey, it is calculated by multiplying the total number of individuals by the probability of the event, giving the expected number who believe in reincarnation.

Sampling and Sample Size

Sampling involves selecting a subset from a population to make inferences. The sample size (here, 100 teens) affects the reliability of estimates. Larger samples tend to provide more accurate reflections of the population proportion.