# Bernoulli experiment and binomial distribution

Part A: A random variable is a numerical value determined by the outcome of an experiment. Briefly describe a discrete random variable. For each of the following indicate whether the random variable is discrete, and provide your reasoning.

i) The distance between Gainesville, Florida, and all Florida cities with population at least 50,000

ii) The number of hits for a team in a high school girls' softball game

iii) The length of time to get a haircut.

iv) The number of cars a jogger passes each morning while running.

Part B:

(a) Describe a Bernoulli experiment and give two examples.

(b) What is the connection between a Bernoulli experiment and a binomial distribution? Explain.

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#### Solution Preview

Part A: A random variable is a numerical value determined by the outcome of an experiment. Briefly describe a discrete random variable. For each of the following indicate whether the random variable is discrete, and provide your reasoning.

A random variable is a quantity whose values are random and to which a probability distribution is assigned. Any situation whose outcome is uncertain is called an experiment. The value of random variable is based on the outcome of the experiment.

A discrete random variable can take finite number of possible values.

i) The distance between Gainesville, Florida, and all Florida cities with population at least 50,000

The distance, measured in miles can take infinite number of possible values and ...

#### Solution Summary

The solution describes a discrete random variable, a Bernoulli experiment and binomial distribution.

Distribution questions

1. What are the assumptions underlying a normal distribution?

2. What are the assumptions underlying a binomial distribution?

3. Why do we want to assume that our sample data represent a

population distribution?

4. What are the differences between the binomial and normal

distributions?

5. What are the similarities between the binomial and normal

distributions?