Assume 10% of all Democrats voted for Trump. If we sample 100 Democrats: 2. 2. D

Question

Assume 10% of all Democrats voted for Trump. If we sample 100 Democrats: 2. 2. Determine the mean of the distribution of sample proportions. a. b. Calculate the standard deviation of the distribution of sample proportions. /00 c. Verify that the distribution of sample proportions is approximately normal nP2s (5) / c0 41 d. Using the normal model approach, find the probability that the sample 25 produces at least 5 Democrats who voted for Trump. (10) Tramp [I5-L num cdCleqqs, .ool,.003) 1 Using the normal model approach, find the probability that the sample produces between 5 and 10 Democrats who voted for Trump. e.

Explanation / Answer

a) mean = p^ = 0.10
b)sd= sqrt(0.1*0.9/100) = 0.03
c) np = 100 *0.1 = 10 > 5
nq = 100*0.9 = 90 > 5
d) P(p^ > 0.05)
=P(Z> (0.05 - 0.10)/0.03))
= P(Z> -1.666666)
= 0.9522

e)
P(5 < X< 10)
=P(0.05 < p^< 0.1)
=P(-1.6666<Z< 0)
= 0.4522

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