document.write( "Question 1138943: Please help with this statistics question\r
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\n" ); document.write( "\n" ); document.write( "In a survey conducted during the previous year by the World Council of
\n" ); document.write( "Engineers it was revealed that 16 out of a random sample of 64 of engineers
\n" ); document.write( "were female. It is assumed that the current rate is persisting worldwide. A sample of 1 000 engineers is selected
\n" ); document.write( "3.2.1 Calculate the probability that at most 375 of them will be female.
\n" ); document.write( "3.2.2 Calculate the probability that at least 420 of them will be female. \n" ); document.write( "

Algebra.Com's Answer #756725 by rothauserc(4718) $\"\"$ $\"About$

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Use the Binomial Probability Formula,
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\n" ); document.write( "Probability(P) (k successes in n trials) = nCk * p^k * (1-p)^(n-k), where nCk = n!/(k! * (n-k)!), p is probability of one success
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\n" ); document.write( "For this problem p = 16/64 = 0.25, n = 1000
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\n" ); document.write( "3.2.1 P(at most 375 will be female) = summation for k from 0 to 375 of 1000Ck * (1/4)^k * (1-(1/4))^(1000-k) = 0.999999
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\n" ); document.write( "3.2.2 P(at least 420 of them will be female) = summation for k from 420 to 1000 of 1000Ck * (1/4)^k * (1-(1/4))^(1000-k) = 0.000001
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