Consider a box model with one 1 and nineteen 0s.If we repeatedly make 10000 draws from the box, and make a histogram of the mean of the draws, what shape would you expect to see?Group of answer choicesA normal distribution with mean 0.05A normal distribution with unknown meanA skewed distribution with mean 0.05A skewed distribution with unknown mean
Question
Consider a box model with one 1 and nineteen 0s.If we repeatedly make 10000 draws from the box, and make a histogram of the mean of the draws, what shape would you expect to see?Group of answer choicesA normal distribution with mean 0.05A normal distribution with unknown meanA skewed distribution with mean 0.05A skewed distribution with unknown mean
Solution
The correct answer is "A normal distribution with mean 0.05".
Here's why:
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The box model is a simple representation of a random process or statistical experiment. In this case, the box contains one 1 and nineteen 0s.
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The mean of the box is calculated as (11 + 190) / 20 = 0.05. This is the expected value of a single draw from the box.
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If we repeatedly draw from the box (with replacement) a large number of times (in this case, 10000 times), the Central Limit Theorem comes into play. This theorem states that the distribution of the sum (or equivalently, the mean) of a large number of independent, identically distributed variables will be approximately normal, regardless of the shape of the original distribution.
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Therefore, if we make a histogram of the mean of the draws, we would expect to see a shape that is approximately normal (bell-shaped), centered around the mean of the box, which is 0.05.
So, the answer is "A normal distribution with mean 0.05".
Similar Questions
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Given the box plot, will the mean or the median provide a better description of the center? (1 point) The mean, because the data distribution is symmetricalThe mean, because the data distribution is pulled to the leftThe median, because the data distribution is pulled to the leftThe median, because the data distribution is pulled to the right6. (05.02 LC)
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What shape does the normal distribution have?
In a normal distribution, what is the shape of the probability density function?Group of answer choices ExponentialU-shapedUniformBell-shaped
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