Flip a coin n=20 times and record the number of heads (9 heads). Knowing that we

Question

Flip a coin n=20 times and record the number of heads (9 heads). Knowing that we can approximate the binomial distribution with a normal distribution with µ=np and 2=np(1-p):

a. Compute µ, for the distribution for a fair coin (p=1/2) and n=20 flips.

b. Compute the z-score of your observation of the number of heads (9). a. -0.44 c. Between which two z-scores (+/-) will roughly 99% of the data be symmetrically distributed around the mean? Using this information, what is the range where we should expect 99% of the number of heads to occur?

d. Compare your number (x) to the range computed above. Does it lie in this range? Is your coin most likely fair or not?

Explanation / Answer

a)
mu = np = 20*0.5 = 10
sigma = sqrt(np(1-p)) = sqrt(20*0.5*0.5) = 2.2361

b)
z = (9 - 10)/2.2361 = -0.4472

c)
z-value for 0.005 area in right tail of the normal curve is given by 2.58

Required range = (10 - 2.58*2.2361, 10 + 2.58*2.2361)
= (4.23, 15.77)

d)
The number 9 lies in this range.
Coin is most likely fair

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