document.write( "Question 1178775: In a 2019 poll of adults 18 years and older, (BBMG Conscious Consumer Report)
\n" ); document.write( "about half of them said that despite tough economic times, they are willing to pay
\n" ); document.write( "more for products that have social and environmental benefits. Suppose that 50% of
\n" ); document.write( "all such adults currently hold this view. Find the probability that in a random sample
\n" ); document.write( "of 20 such adults, the number of adults in this sample who hold this opinion is:
\n" ); document.write( "a. none [2 marks]
\n" ); document.write( "b. exactly 10 [2 marks]
\n" ); document.write( "c. at most 7 [2 marks]
\n" ); document.write( "d. more than 10 [3 marks]
\n" ); document.write( "e. at least 13 [3 marks]
\n" ); document.write( "f. 12 to 15 (inclusive) [3 marks] \n" ); document.write( "
Algebra.Com's Answer #808197 by ikleyn(52817)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( " In a 2019 poll of adults 18 years and older, (BBMG Conscious Consumer Report)
\n" ); document.write( "about half of them said that despite tough economic times, they are willing to pay
\n" ); document.write( "more for products that have social and environmental benefits. Suppose that 50% of
\n" ); document.write( "all such adults currently hold this view. Find the probability that in a random sample
\n" ); document.write( "of 20 such adults, the number of adults in this sample who hold this opinion is:
\n" ); document.write( "a. none
\n" ); document.write( "b. exactly 10
\n" ); document.write( "c. at most 7
\n" ); document.write( "d. more than 10
\n" ); document.write( "e. at least 13
\n" ); document.write( "f. 12 to 15 (inclusive)
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document.write( "      All these questions are about binomial distribution probability problems.\r\n" );
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document.write( "      In all these cases you need calculate the probability P(n,k,p), where\r\n" );
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document.write( "           - number of trials         n =  20;\r\n" );
document.write( "           - Probability of success on a single trial p = 0.5;\r\n" );
document.write( "           - k is the number of success trials, which varies from case to case.\r\n" );
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document.write( "      To facilitate calculations, I use an online (free of charge) calculator at this web-site \r\n" );
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document.write( "      https://stattrek.com/online-calculator/binomial.aspx\r\n" );
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document.write( "      It provides nice instructions  and  a convenient input and output for all relevant options/cases.\r\n" );
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document.write( "(a)  \"none\" means 0 (zero) susccessful trials k=0.\r\n" );
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document.write( "      So, in this case you need calculate  P(n=20; k=0; p=0.5).\r\n" );
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document.write( "      The calculators gives  P(n=20; k=0; p=0.5) = \"0.5%5E20\" = 9.53674E-07.         ANSWER\r\n" );
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document.write( "(b)   In this case you need calculate  P(n=20; k=10; p=0.5).\r\n" );
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document.write( "      The calculators gives  P(n=20; k=10; p=0.5) = 0.1762   (rounded).           ANSWER\r\n" );
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document.write( "(c)   In this case you need calculate  P(n=20; k<=7; p=0.5).\r\n" );
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document.write( "      The calculators gives  P(n=20; k<=7; p=0.5) = 0.1316   (rounded).           ANSWER\r\n" );
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document.write( "(d)   In this case you need calculate  P(n=20; k>10; p=0.5).\r\n" );
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document.write( "          * * * Do it ON YOUR OWN, as instructed. * * * \r\n" );
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document.write( "(e)   In this case you need calculate  P(n=20; k>=13; p=0.5).\r\n" );
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document.write( "          * * * Do it ON YOUR OWN, as instructed. * * * \r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, I stop my teaching.\r
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\n" ); document.write( "\n" ); document.write( "To see a variety of similar solved problems,  look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Simple and simplest probability problems on Binomial distribution \r
\n" ); document.write( "\n" ); document.write( "    - Typical binomial distribution probability problems \r
\n" ); document.write( "\n" ); document.write( "    - How to calculate Binomial probabilities with Technology (using MS Excel) \r
\n" ); document.write( "\n" ); document.write( "    - Solving problems on Binomial distribution with Technology (using MS Excel) \r
\n" ); document.write( "\n" ); document.write( "    - Solving problems on Binomial distribution with Technology (using online solver) \r
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\n" ); document.write( "\n" ); document.write( "After reading these lessons,  you will be able to solve such problems on your own, \r
\n" ); document.write( "\n" ); document.write( "which is your  PRIMARY  MAJOR  GOAL  visiting this forum  (I believe).\r
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