SOLUTION: about 80% of the residents of the united states are right-handed. if 1000 residents are selected at random, would it be unusual to find that fewer than 77%of the resident in the sa

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Question 533783: about 80% of the residents of the united states are right-handed. if 1000 residents are selected at random, would it be unusual to find that fewer than 77%of the resident in the sample are right-headed?
Answer by reviewermath(1029) About Me  (Show Source):
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Solution using Binomial Distribution (Exact Solution)
X~Binomial(n=1000,p=0.8)
77% of 1000 = 770, use 769 as upper limit
probability that fewer than 77% of the resident in the sample are right-headed is equal to

Solution using Normal Distribution (Approximate Solution)
mu+=+np+=+1000%280.8%29+=+800
+sigma%5E2+=+npq+=+1000%280.8%29%280.2%29+=+160
we use continuity correction by adding 0.5 to 769
P%28X%3C=769.5%29+=+P%28Z%3C=%28769.5-800%29%2Fsqrt%28160%29%29
=P%28Z%3C=-2.4112%29
= highlight%280.00795%29
It is unusual to find that fewer than 77% of the resident in the sample are right-headed because the probability is less than 0.05.