assign numerical values to coin flips: Heads is +1 and Tails is –1, each with probability 1⁄2. After a huge number of coin flips, you’d expect an average value of
Let’s assign numerical values to coin flips: Heads is +1 and Tails is –1, each with probability 1⁄2.
After a huge number of coin flips, you’d expect an average value of ? = 0, because you’d expect roughly as many Heads (+1) as Tails (-1), so on average they would cancel out to 0. Since Heads and Tails are both 1 unit of deviation away from the mean, the standard deviation is just ? = 1.
Suppose that you flip a coin ? = 100 times.
If you get 49 Heads and 51 Tails, what is the “mean coin flip score” ?̅? Hint: just apply the usual
definition of mean: add up all the values, with +1 for each Head and –1 for each Tail, then divide by 100.
the answer to part (a) is ?̅ = −0.02. Use this to answer the following: what is the probability that, if you flip a coin 100 times, you get 49 Heads or fewer? Hint: calculate the z-score for this sample, using ? = (?̅ − ?) / (?/√?), and then use the chart.
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