document.write( "Question 1198046: Business Weekly conducted a survey of recent graduates from the top MBA programs. On the basis of the survey, assume that 75% of the recent graduates annual salary exceeds $75000. Suppose you take a simple random sample of 86 recent graduates.\r
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Algebra.Com's Answer #831549 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Business Weekly conducted a survey of recent graduates from the top MBA programs.
\n" ); document.write( "On the basis of the survey, assume that 75% of the recent graduates annual salary exceeds $75000.
\n" ); document.write( "Suppose you take a simple random sample of 86 recent graduates.
\n" ); document.write( "Find the probability that more than 85% of the 86 recent graduates have an annual salary exceeding $75000.
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document.write( "This problem is a binomial distribution with the number of trials n= 86,\r\n" );
document.write( "the probability of the individual success p= 75% = 0.75 and the number of \r\n" );
document.write( "succesful trials k > 0.85*86 = 73.1.\r\n" );
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document.write( "Since n*p = 86*p.75 = 73.1 is greater than 5 and since n*(1-p) = 86*0.15 = 12.9 is greater than 5,\r\n" );
document.write( "the basis is provided to apply the normal approximation to the binomial approximation.\r\n" );
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document.write( "So, we take the normal distribution with the mean m= p*n = 0.85*86 = 73.1 and the standard\r\n" );
document.write( "deviation SD =  =  = 3.3113  (rounded).\r\n" );
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document.write( "It is the normal distribution which we use as an approximation.\r\n" );
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document.write( "Now the probability under the problem's question is the are under the this specified normal curve \r\n" );
document.write( "to the RIGHT of the mark of 73.5 (the continuity correction).\r\n" );
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document.write( "You can use your calculator's standard function normalcdf(73.5,9999,73.1,3.3113)\r\n" );
document.write( "or the Internet's free of charge online calculator https://onlinestatbook.com/2/calculators/normal_dist.html\r\n" );
document.write( "to get the  ANSWER  P = 0.4519.\r\n" );
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document.write( "You may also want to calculate this probability directly as the binomial probability.\r\n" );
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document.write( "In this case, use an online free of charge calculator https://stattrek.com/online-calculator/binomial\r\n" );
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document.write( "    P(n= 86, k> 73, p= 0.85) = 0.46596.\r\n" );
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document.write( "Both values are quite close, giving you the needed confidence.\r\n" );
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