document.write( "Question 1166570: According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select six peanut M&M’s from an extra-large bag of the candies. (Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.)\r
\n" ); document.write( "\n" ); document.write( "Compute the probability that exactly three of the six M&M’s are blue. \r
\n" ); document.write( "\n" ); document.write( "Compute the probability that three or four of the six M&M’s are blue. \r
\n" ); document.write( "\n" ); document.write( "Compute the probability that at most three of the six M&M’s are blue. \r
\n" ); document.write( "\n" ); document.write( "Compute the probability that at least three of the six M&M’s are blue. \r
\n" ); document.write( "\n" ); document.write( "If you repeatedly select random samples of six peanut M&M’s, on average how many do you expect to be blue? (Round your answer to two decimal places.)
\n" ); document.write( " blue M&M’s\r
\n" ); document.write( "\n" ); document.write( "With what standard deviation? (Round your answer to two decimal places.)
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Algebra.Com's Answer #852713 by ikleyn(53313) $\"\"$ $\"About$

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\n" ); document.write( "According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow,
\n" ); document.write( "12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select six peanut M&M’s
\n" ); document.write( "from an extra-large bag of the candies. (Round all probabilities below to four decimal places;
\n" ); document.write( "i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.)\r
\n" ); document.write( "\n" ); document.write( "(a) Compute the probability that exactly three of the six M&M’s are blue.
\n" ); document.write( "(b) Compute the probability that three or four of the six M&M’s are blue.
\n" ); document.write( "(c) Compute the probability that at most three of the six M&M’s are blue.
\n" ); document.write( "(d) Compute the probability that at least three of the six M&M’s are blue.
\n" ); document.write( "(e) If you repeatedly select random samples of six peanut M&M’s, on average how many do you expect to be blue?
\n" ); document.write( " (Round your answer to two decimal places.)
\n" ); document.write( "(f) With what standard deviation? (Round your answer to two decimal places.)
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document.write( "(a)  In this case, we have a binomial distribution with n=6 trials, k=3 successful trials.\r\n" );
document.write( "     p=0.23 probability of the individual success in each trial.  Apply the standard formula for this probability\r\n" );
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document.write( "        P =  =  = 0.1111 (rounded).   ANSWER\r\n" );
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document.write( "(b)  In this case\r\n" );
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document.write( "        P = P(3) + P(4) =  +  = \r\n" );
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document.write( "                        =  = 0.1360  (rounded).    ANSWER\r\n" );
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document.write( "(c)  Continue in the same style\r\n" );
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document.write( "        P = P(0) + P(1) + P(2) + P(3) = . . . = 0.972  (rounded).    ANSWER\r\n" );
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document.write( "     To replace monotonic calculations, you may use very convenient online calculator\r\n" );
document.write( "     https://stattrek.com/online-calculator/binomial/\r\n" );
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document.write( "(d)  Continue in the same style\r\n" );
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document.write( "        P = P(3) + P(4) + P(5) + P(6) = 1 - ( P(0) + P(1) + P(2) ) = 1 - 0.8609 = 0.1391  (rounded).    ANSWER\r\n" );
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document.write( "     To replace monotonic calculations, you may use very convenient online calculator\r\n" );
document.write( "     https://stattrek.com/online-calculator/binomial/\r\n" );
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document.write( "(e)  Mathematical expectation is  n*p = 6*0.23 = 1.38 blue peanuts.\r\n" );
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document.write( "(f)  With the standard deviation  SD =  =  = 1.0308  (rounded).    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved: all questions are answered.\r
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