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

Emily-Jane Bray

Emily-Jane Bray

Answered question

2021-02-16

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

Answer & Explanation

Sally Cresswell

Sally Cresswell

Skilled2021-02-17Added 91 answers

Step 1 
Normal approximation to the binomial: 
It is evident from the facts provided 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) and nq(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 
Consequently, the x distribution is normal with mean. 52 and standard deviation 5.099.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-11Added 2605 answers

Answer is given below (on video)

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