# A fair coin is flipped 104 times. Let x be the number of heads. What normal distributions best approximates x?

A fair coin is flipped 104 times. Let x be the number of heads. What normal distributions best approximates x?
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Sally Cresswell
Step 1
Normal approximation to the binomial:
From the given information, it is clear that sample size, n = 104.
The probability of success, p = 0.5.
The probability of failure, q = 1 – 0.5 = 0.50
Since $np\left(104×0.5=52\right)\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}nq\left(104×0.5=52\right)$ are greater than 5, normal approximation to the binomial can be done.
Step 2
Mean and standard deviation of the distribution:
The mean and standard deviation are calculated as follows.
Mean, $\mu =n×p$
$=104×0.5$
=52
Standard deviation, $\sigma =\sqrt{n×p×q}$
$=\sqrt{104×0.50×0.50}$
=5.099
Thus, the distribution of x follows normal with mean 52 and standard deviation 5.099.
Jeffrey Jordon