1. Wishing to test the claim that a certain coin is “fair”: You toss the coin 25
ID: 3237673 • Letter: 1
Question
1. Wishing to test the claim that a certain coin is “fair”: You toss the coin 250 times, and get 140 heads. Using the appropriate Binomial Distribution model for a fair coin, find the following values:
a.) The mean and standard deviation of the sample heads count X, for the 250 tosses.
b.) The difference d between the heads count X from your test, and the expected heads count.
c.) The percent probability that X would fall at least d away from expected, in the positive direction.
d.) The percent probability that X would fall at least d away from expected, in either direction.
2. Refer back to the completed coin-toss experiment data, using the Central Limit Theorem and the appropriate Normal Distribution Model for a fair coin, find the following values:
a. The mean and standard deviation of the sample proportion pof heads, for the 250 tosses.
b. The difference d between the heads proportion pfrom your test, and the expected heads proportion.
c. The percent probability that pwould fall at least d away from expected, in the positive direction.
d. The percent probability that pwould fall at least d away from expected, in either direction.
Explanation / Answer
Solution:
a)
Bionomial distribution with
n = 250
p=1/2
mean = n*p = 250*1/2 = 125
standard deviation = sqrt(n*p*(1-p) = sqrt(250*1/2*1/2) = 7.9
b)
Expected value of Heads = E(H) = n*P(H) = 250*1/2 = 125
so,
d = 140-125 = 15
c)
probability that X would fall at least d away from expected, in the positive direction = P(X>140)
= 1-P(X<140)
= 1 - P(Z<(140-125)/7.9)
= 1- P(Z<1.89)
= 1-0.97
=0.03
d)
probability that X would fall at least d away from expected, in either direction
= P(X<(125-15))+P(X>140)
=P(X<110)+P(X>140)
=P(Z<(110-125)/7.9)+0.03
=0.03+0.03
=0.06
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