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

Emily-Jane Bray 2021-02-16 Answered
A fair coin is flipped 104 times. Let x be the number of heads. What normal distributions best approximates x?
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Expert Answer

Sally Cresswell
Answered 2021-02-17 Author has 91 answers
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(104×0.5=52)andnq(104×0.5=52) 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, μ=n×p
=104×0.5
=52
Standard deviation, σ=n×p×q
=104×0.50×0.50
=5.099
Thus, the distribution of x follows normal with mean 52 and standard deviation 5.099.
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Jeffrey Jordon
Answered 2021-11-11 Author has 2047 answers

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