The margin of error ________ (increases or decreases) with an increased sample size and ________ (increases or decreases) with a
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Answer:
We assume that we have a fair coin that is
For this case we define the random variable X as "number of heads observed in 20 times". The distribution for X is given by:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Step-by-step explanation:
Previous concepts
A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Solution to the problem
We assume that we have a fair coin that is
For this case we define the random variable X as "number of heads observed in 20 times". The distribution for X is given by:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula: