One thousand coins were flipped eight times and the number of heads was recorded for each coin. The results are as follows: Number of hea
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The question is based on goodness of fit.
One thousand coins were flipped eight times and the number of heads was recorded for each coin. The results are as follows:
|
Number of heads |
Number of coins |
|
0 |
6 |
|
1 |
32 |
|
2 |
105 |
|
3 |
186 |
|
4 |
236 |
|
5 |
201 |
|
6 |
98 |
|
7 |
33 |
|
8 |
103 |
1.Test whether the distribution of coin flips matches the expected frequencies from a binomial distribution assuming all fair coins. (A coin is fair if the probability of heads per flip is 0.5)
2.If the binomial distribution is a poor fit to the data, identify in what way the distribution does not match the expectation.
3.Some two-headed coins (which always show heads on every flip) were mixed in with the fair coins. Can you say approximately how many two-headed there might have been out of this 1000?
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