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You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "YOUR PROBLEM:\r\n" );
document.write( "Five out of 50 people called to give money to a charity actually agrees to give money. Based \r\n" );
document.write( "on this percentage, what is the probability that out of the next 25 people called:\r\n" );
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document.write( "a. Exactly 1 agrees to give money?\r\n" );
document.write( "b. At least two agree to give money?\r\n" );
document.write( "c. At most 5 agree to give money?\r\n" );
document.write( "d. More than 3 agree to give money?\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "This situation can be modeled by the binomial distribution because we are interested in the \r\n" );
document.write( "number of successes in a series of independent trials (yes/no experiments). \r\n" );
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document.write( "x = random variable = the event that a person agrees to give money\r\n" );
document.write( "n = sample size = 25 people\r\n" );
document.write( "p = probability of success = 5/50 = 0.10\r\n" );
document.write( "q = probability of failure = 45/50 = 0.90\r\n" );
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document.write( "The probability distribution formula:\r\n" );
document.write( "P(x=k) = [nCk]\r\n" );
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document.write( "a) The probability that exactly one person agrees to give money:\r\n" );
document.write( "In this case, k = 1 so we have\r\n" );
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document.write( "P(x=1) = [25C1] \r\n" );
document.write( "P(x=1) = [25]*{0.0797665531]\r\n" );
document.write( "P(x=1) = 0.1994161077\r\n" );
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document.write( "b) The probability that at least two people agree to give money:\r\n" );
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document.write( "\"at least two people\" means two people or more than two people. No people (x=0) or one \r\n" );
document.write( "person (x=1) agreeing do not qualify as \"at least two.\" \r\n" );
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document.write( "We calculate this probability by adding the applicable probabilities, \r\n" );
document.write( "P(x=2) + P(x=3) + … + P(x=24) + P(x=25). \r\n" );
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document.write( "That's a lot of calculating. Recall that the sum of all probabilities is 1.00. Therefore, we can \r\n" );
document.write( "simplify our calculations by calculating \r\n" );
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document.write( "1.00 - P(x=0) - P(x=1). \r\n" );
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document.write( "Do you see why this works? Either method you use will give the same probability.\r\n" );
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document.write( "I'll leave it to you to set up the equation and make the calculations.\r\n" );
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document.write( "c. At most 5 agree to give money:\r\n" );
document.write( "What does \"at most 5 people\" mean? Sum up the applicable probabilities just as you did in (b).\r\n" );
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document.write( "d. More than 3 agree to give money?\r\n" );
document.write( "How many can \"more than three\" be? Once you determine that, you need to add the \r\n" );
document.write( "appropriate probabilities as you did in part (b). THere is a shortcut equation for this one too.\r\n" );
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document.write( "Good luck! Feel free to email if you have further questions about this problem.\r\n" );
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document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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