Algebra.Com's Answer #844203 by ikleyn(52914)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "According to The World Bank, only 9% of the population of Uganda had access to electricity as of 2009.
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document.write( "Suppose we randomly sample 145 people in Uganda. Let X = the number of people who have access to electricity.
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document.write( "(a) What is the probability distribution for X?
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document.write( "X ~ G(145)
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document.write( "X ~ B(145, 0.09)
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document.write( "X ~ P(0.09)
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document.write( "X ~ G(0.09)
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document.write( "X ~ B(0.09, 145)
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document.write( "(b) Using the formulas, calculate the mean and standard deviation of X.
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document.write( "(Enter your mean to two decimal places and round your standard deviation to four decimal places.)
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document.write( "(c) Use your calculator to find the probability that 15 people in the sample have access to electricity.
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document.write( "(Round your answer to four decimal places.)
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document.write( "(d) Find the probability that at most ten people in the sample have access to electricity.
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document.write( "(Round your answer to four decimal places.)
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document.write( "(e) Find the probability that more than 25 people in the sample have access to electricity.
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document.write( "(Round your answer to four decimal places.)
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document.write( "(a) It is a binomial distribution with n= 145 trials and the probability of success p= 0.09 \r\n" );
document.write( " for each individual trial.\r\n" );
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document.write( " I do not understand the meaning of these hieroglyphs under (a), so you should determine it on your own.\r\n" );
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document.write( "(b) The mean for this binomial distribution is m = n*p = 0.09*145 = 13.05.\r\n" );
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document.write( " The standard deviation is SD =  =  = 3.446084735.\r\n" );
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document.write( "Questions (c), (d) and (e) assume that you will use normal distribution formulas for this binomial distribution \r\n" );
document.write( "as an approximation. Statistically, it is possible because the number of trials n= 145 is great.\r\n" );
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document.write( "(c) Use your regular calculator TI-83/84 with standard function normcdf \r\n" );
document.write( " (which stands for Cumulative Distribution Function).\r\n" );
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document.write( " For (c), the probability is the area under the normal curve (with the mean and standard deviation determined in (a))\r\n" );
document.write( " in the interval (14.5,15.5). This interval \"with plus/minus halves\" is the continuous correction, when we use normal\r\n" );
document.write( " distribution as an approximation to binomial. So, we write\r\n" );
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document.write( " z1 z2 mean SD <<<---=== formatting pattern\r\n" );
document.write( " P = normcdf( 14.5, 15.5, 13.05, 3.446084735).\r\n" );
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document.write( " Alternatively, you may use free of charge online calculator for normal distribution\r\n" );
document.write( " https://onlinestatbook.com/2/calculators/normal_dist.html\r\n" );
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document.write( " To be honest, I always use it in my calculations, since it has simple and very convenient interface\r\n" );
document.write( " and great visual output.\r\n" );
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document.write( " You can be restricted in using calculators, so use whichever is an appropriate for you.\r\n" );
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document.write( " In any case, the answer for (c) is P = 0.0984.\r\n" );
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document.write( "(d) For (d), the probability is the area under the normal curve (with the mean and standard deviation determined in (a))\r\n" );
document.write( " in the interval ( , ). This interval is the continuous correction to \"at most 10\", when we use normal\r\n" );
document.write( " distribution as an approximation to binomial. So, we write\r\n" );
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document.write( " z1 z2 mean SD <<<---=== formatting pattern\r\n" );
document.write( " P = normcdf( -9999, 10.5, 13.05, 3.446084735).\r\n" );
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document.write( " Again, alternatively, you may use free of charge online calculator for normal distribution\r\n" );
document.write( " https://onlinestatbook.com/2/calculators/normal_dist.html\r\n" );
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document.write( " In any case, the answer for (d) is P = 0.2297.\r\n" );
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document.write( "(e) For (e), the probability is the area under the normal curve (with the mean and standard deviation determined in (a))\r\n" );
document.write( " in the interval ( , ). This interval is the continuous correction to \"more than 25\", when we use normal\r\n" );
document.write( " distribution as an approximation to binomial. So, we write\r\n" );
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document.write( " z1 z2 mean SD <<<---=== formatting pattern\r\n" );
document.write( " P = normcdf( 25.5, 9999, 13.05, 3.446084735).\r\n" );
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document.write( " Again, alternatively, you may use free of charge online calculator for normal distribution\r\n" );
document.write( " https://onlinestatbook.com/2/calculators/normal_dist.html\r\n" );
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document.write( " In any case, the answer for (e) is P = 0.0002.\r\n" );
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document.write( " It is a vanishing value; when the value of probability is vanishing, normal approximation works badly \r\n" );
document.write( " (consider it as my warning to you).\r\n" );
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document.write( "At this point, I complete my solution.\r
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document.write( "It is not a simple task to write so long text - - - so, I do not like posts with many questions.\r
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document.write( "The rules of this site/forum say \"One and ONLY ONE question per post\".\r
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document.write( "OK, three inter-connected questions are still possible, but 5 is definitely tooooooooooooo much.\r
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