document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #351162 by reviewermath(1029) $\"\"$ $\"About$

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Solution using Binomial Distribution (Exact Solution)
\n" ); document.write( "X~Binomial(n=1000,p=0.8)
\n" ); document.write( "77% of 1000 = 770, use 769 as upper limit
\n" ); document.write( "probability that fewer than 77% of the resident in the sample are right-headed is equal to
\n" ); document.write( "

\n" ); document.write( "Solution using Normal Distribution (Approximate Solution)
\n" ); document.write( " $\"mu+=+np+=+1000%280.8%29+=+800\"$
\n" ); document.write( " $\"+sigma%5E2+=+npq+=+1000%280.8%29%280.2%29+=+160\"$
\n" ); document.write( "we use continuity correction by adding 0.5 to 769
\n" ); document.write( " $\"P%28X%3C=769.5%29+=+P%28Z%3C=%28769.5-800%29%2Fsqrt%28160%29%29\"$
\n" ); document.write( " = $\"P%28Z%3C=-2.4112%29\"$
\n" ); document.write( " = $\"highlight%280.00795%29\"$ \r
\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "

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