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Chapter 6: Problem 6

Explain what "success" means in a binomial experiment.

Short Answer

Expert verified
'Success' in a binomial experiment is the specified outcome of interest that we are counting, like getting a heads in coin flips.

Step by step solution

01

Understand a Binomial Experiment

A binomial experiment is a statistical experiment that has the following characteristics: the experiment consists of a fixed number of trials, each trial has only two possible outcomes (success and failure), the probability of success is the same for each trial, and the trials are independent.
02

Define the Term 'Success'

In the context of a binomial experiment, 'success' refers to one of the two outcomes of a trial. It is the outcome of interest that we are counting. For example, if we are flipping a coin and interested in the number of times it lands on heads, then landing on heads would be considered a 'success'.
03

Provide Examples

To clarify, consider some examples: If we roll a die and are interested in the number of times a '4' appears, a '4' is the success outcome. If we conduct a survey where we want to know if people prefer tea over coffee, each 'yes' response can be considered a success.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

success in binomial experiment
In the realm of statistics, a binomial experiment is defined by a set of characteristics that include a fixed number of trials, consistent probabilities for the outcomes, and each trial being independent of the others. Within this framework, the term 'success' carries a specific meaning. It refers to the outcome of interest in each trial, the result we are counting.
probability of success
The probability of success in a binomial experiment is the chance that the outcome of interest will occur in a single trial. It's essential for this probability to remain constant across all trials. For example, when flipping a fair coin, the probability of success (getting heads) is 0.5 for every flip. This consistent probability enables accurate statistical predictions and calculations involving binomial experiments.
independent trials
A key element of binomial experiments is that the trials are independent. This means that the result of any one trial does not affect the outcome of any other trial. If we are rolling a fair die, the outcome of one roll does not influence the next roll鈥檚 outcome. This independence ensures the statistical integrity of the binomial model and allows for the straightforward application of probability rules.

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Most popular questions from this chapter

Suppose a life insurance company sells a \(\$ 250,000\) one-year term life insurance policy to a 20 -yearold male for \(\$ 350 .\) According to the National Vital Statistics Report, Vol. \(53,\) No. \(6,\) the probability that the male survives the year is \(0.998611 .\) Compute and interpret the expected value of this policy to the insurance company.

High-Speed Internet According to a report by the Commerce Department in the fall of \(2004,20 \%\) of U.S. households had some type of high-speed Internet connection. Suppose 20 U.S. households are selected at random and the number of households with high-speed Internet is recorded. (a) Find the probability that exactly 5 households have high-speed Internet. (b) Find the probability that at least 10 households have high-speed Internet. Would this be unusual? (c) Find the probability that fewer than 4 households have high-speed Internet. (d) Find the probability that between 2 and 5 households, inclusive, have high-speed Internet.

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of lightbulbs that burn out in the next week in a room of with 20 bulbs. (b) The time it takes to fly from New York City to Los Angeles. (c) The number of hits to a Web site in a day. (d) The amount of snow in Toronto during the winter.

Determine whether the distribution is a discrete probability distribution. If not, state why. $$\begin{array}{|l|l|} \hline x & f(x) \\ \hline 0 & 0.2 \\ \hline 1 & 0.2 \\ \hline 2 & 0.2 \\ \hline 3 & 0.2 \\ \hline 4 & 0.2 \\ \hline \end{array}$$

Determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why. An experimental drug is administered to 100 randomly selected individuals, with the number of individuals responding favorably recorded.
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