document.write( "Question 1131283: Survey is 40% random sample is 250 we need to find the probability
\n" ); document.write( "Exactly 95
\n" ); document.write( "Between 105 and 110
\n" ); document.write( "At most 85
\n" ); document.write( "At least 95 for at least 95 you subtract 1 and did 94 but how is that possible when at least 95 will be 95 up to 250? \n" ); document.write( "

Algebra.Com's Answer #747944 by Boreal(15235) $\"\"$ $\"About$

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If the probability is exactly 40%, then the mean is np=100 and the variance np(1-p) or 100*.6=24 and the sd sqrt (24)=4.90
\n" ); document.write( "exactly 95 is 250C95*.4^95*.6^155=0.0421
\n" ); document.write( "using normal approximation, this is (94.5-100)/4.90 and (95.5-100)/4.9 or z between -1.12 and -0.92 for a probability of 0.0474\r
\n" ); document.write( "\n" ); document.write( "between 105 and 110 I would use the normal approximation using 105.5 and 109.5 unless it included 105 and 110, and then I would use 104.5 and 110.5. There are two possible answers. Using the first, it would be
\n" ); document.write( "z=(105.5-100)/4.9 or +1.12 and z=9.5/4.9 or 1.94
\n" ); document.write( "This has a probability of 0.1052\r
\n" ); document.write( "\n" ); document.write( "at most 85 is z < (84.5-100)/4.9 or z<=-3.16 and probability of 0.0008
\n" ); document.write( "at least 95, I would use (94.5-100)/4.9 or z>-1.12 which is 0.8686 \n" ); document.write( "

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