My question comes from an example in Mathematical Statistics and Data Analysis 3rd edition by John Rice. The following screenshot is the discussion of the example:
My question is with the interpretation of the final answer. The example says that: "The probability is rather small, so the fairness of the coin is called into question."
My take on this is, if we are evaluating the probability of a deviation as extreme or more extreme than 60, wouldn't we want a smaller probability (if we are assuming our coin is fair)? Wouldn't we want the probability of anything deviating from our "fair" evaluation of 50 to be small? Now imagining the distribution of head flips visually in terms of a normal distribution, I could see what is being meant. But I'm finding a disconnect in the understanding.