Heads occurs 15 times out of 20 - Is it a fair coin?

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The discussion centers on determining whether a coin is fair after observing 15 heads in 20 flips. The textbook states that 96% of the time, the number of heads in 20 flips will fall between 6 and 14, prompting a request for proof of this statistic. To validate the 96% figure, one must calculate the probabilities for obtaining exactly 6 to 14 heads using binomial distribution. The concept of a fair coin is defined as one that yields heads and tails in equal proportions over a large number of flips. Ultimately, the fairness of the coin remains in question based on the observed results.
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Homework Statement



I have to answer this question by using references to expectation and probability as well as any other relevant considerations. My textbook says that 96% of the time, the number of heads in 20 flips will be between 6 and 14 inclusive. How do I prove this?
 
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Do you know about the standard deviation?
 
phono said:
My textbook says that 96% of the time, the number of heads in 20 flips will be between 6 and 14 inclusive. How do I prove this?
Even if you answer this, it won't tell you the answer to the question in the thread title. Are you sure you gave us all the information?

Anyway, if you want to prove that 96% figure, you have to add up the probabilities for "exactly 6", "exactly 7" and so on. Do you know how to calculate those?
 
Heads occurs 15 times out of 20 - Is it a fair coin?

A fair coin is one which gives 50% heads and 50% tale when tossed for infinite number of times.
 

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