document.write( "Question 1208472: The chance that a U.S. police chief believes the death penalty “significantly reduces the number of homicides” is 1 in 4. If a random sample of 8 police chiefs is selected, find the probability that at most 3 believe that the death penalty significantly reduces the number of homicides. \n" ); document.write( "
Algebra.Com's Answer #846910 by math_tutor2020(3816)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "Answer: 0.88618 (approximate)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "--------------------------------------------------------------------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Quick way to find the answer using technology\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "On a TI83 or similar, you would use the BinomCDF command. \n" ); document.write( "The order of inputs is: n, p, k n = number of trials = 8\r\n" ); document.write( "p = probability of success = 0.25\r\n" ); document.write( "k = number of successes = 3Type in BinomCDF(8,0.25,3) to get the approximate result 0.88618 \n" ); document.write( "The answer will vary depending how you round it.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Here are some alternative technology options.
\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "--------------------------------------------------------------------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The slightly longer method\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The binomial probability formula is \n" ); document.write( "B(x) = (nCx)*(p^x)*(1-p)^(n-x) \n" ); document.write( "where, n = number of trials\r\n" ); document.write( "p = probability of success\r\n" ); document.write( "x = number of successesThe nCx refers to the nCr combination formula. These values are found in Pascal's Triangle. A quick way to calculate the nCr values is to use the Combin function in a spreadsheet. Or you can use a TI Calculator. \n" ); document.write( "Like with many things in math, there are many options to calculate nCr.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Let's calculate the probability of exactly 0 police chiefs believe that the death penalty significantly reduces the number of homicides. \n" ); document.write( "B(x) = (nCx)*(p^x)*(1-p)^(n-x) \n" ); document.write( "B(x) = (8Cx)*(0.25^x)*(1-0.25)^(8-x) \n" ); document.write( "B(0) = (8C0)*(0.25^0)*(1-0.25)^(8-0) \n" ); document.write( "B(0) = (1)*(0.25^0)*(1-0.25)^(8-0) \n" ); document.write( "B(0) = 0.10011292 \n" ); document.write( "This value is approximate. \n" ); document.write( "It is possible to calculate by hand, given a very long time, but I recommend a calculator. \r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Repeat the process to find these other values \n" ); document.write( "B(1) = 0.26696777 \n" ); document.write( "B(2) = 0.3114624 \n" ); document.write( "B(3) = 0.2076416 \n" ); document.write( "I'll skip showing the steps for these. \r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Therefore, \n" ); document.write( "B(0)+B(1)+B(2)+B(3) \n" ); document.write( "= 0.10011292+0.26696777+0.3114624+0.2076416 \n" ); document.write( "= 0.88618469 \n" ); document.write( "= 0.88618 \n" ); document.write( "The answer will vary depending how you round it.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "More practice with the Binomial Distribution is found on this page \n" ); document.write( " \n" ); document.write( " |