document.write( "Question 1197774: 750 eggs are randomly sampled from a population where 14% of all eggs are fertilized. Use the normal approximation to the binomial to find the following probabilities rounded to 3 decimal places.\r
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\n" ); document.write( "\n" ); document.write( "a. Find the probability that exactly 106 of the eggs are fertilized.\r
\n" ); document.write( "\n" ); document.write( "b. Find the probability that at least 106 of the eggs are fertilized.\r
\n" ); document.write( "\n" ); document.write( "c. Find the probability that fewer than 106 of the eggs are fertilized.\r
\n" ); document.write( "\n" ); document.write( "d. Find the probability that between 104 and 106, inclusive, of the eggs are fertilized. \n" ); document.write( "

Algebra.Com's Answer #831193 by ewatrrr(24785) $\"\"$ $\"About$

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document.write( "Hi  \r\n" );
document.write( "Binomial distribution:  p - .14,  n = 750\r\n" );
document.write( "Using the normal approximation and the NOted continuity correction factor.\r\n" );
document.write( "(the continuity correction factor used as a Binomial Distribution is not continuous)\r\n" );
document.write( "µ = .14*750 = 105,  and σ =  = 9.5026 \r\n" );
document.write( "Using TI or similarly an inexpensive calculator like an Casio fx-115 ES plus\r\n" );
document.write( "a. P(x = 106) = binompdf(750,.14,106) = .042  0r normpdf( 106,105,9.5026) = .042\r\n" );
document.write( "          with continuity correction factor,  normcdf(105.5,106.5, 9.5026, 105)=.042                         \r\n" );
document.write( "b. P x ≥ 106) = normcdf(105.5,9999, 9.5026, 105) = .479\r\n" );
document.write( "c. P(x<106) = P(x <105.5) = normcdf(-9999,105.5, 9.5026, 105)= .521\r\n" );
document.write( "d. P(104 ≤ x ≤ 106) =  normcdf(103.5,106.5, 9.5026, 105) =.1254\r\n" );
document.write( "Wish You the Best in your Studies.\r\n" );
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