document.write( "Question 1197441: Bowling is being played by Ana and Bea. Assume that both are experienced bowlers and that Bea's and Ana's bowling scores are regularly distributed, with Ana's having a mean of 175 and a standard deviation of 10, and Bea's having a mean of 170 and a standard deviation of 5. determine the likelihood that\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(A) At least one of them registers a game-high 185 points.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(B) Ana and Bea both receive scores of between 168 and 173. \n" ); document.write( "

Algebra.Com's Answer #830779 by ikleyn(52810) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Bowling is being played by Ana and Bea. Assume that both are experienced bowlers and that Bea's and Ana's bowling scores
\n" ); document.write( "are regularly distributed, with Ana's having a mean of 175 and a standard deviation of 10,
\n" ); document.write( "and Bea's having a mean of 170 and a standard deviation of 5. determine the $\"highlight%28cross%28likelihood%29%29\"$ probability that\r
\n" ); document.write( "\n" ); document.write( "(A) At least one of them registers a game-high 185 points.\r
\n" ); document.write( "\n" ); document.write( "(B) Ana and Bea both receive scores of between 168 and 173.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            The solution in the post by @ewatrrr is incorrect for question (A).\r
\n" ); document.write( "\n" ); document.write( "            So, I came to bring you a correct solution to this question.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "                        Part (A)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "P(Ana above 185) = P_normal (µ = 175; σ = 10; above 185) = 0.1587 (use your calculator or any tool which you like).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "P(Bea above 185) = P_normal](µ = 170; σ =  5; above 185) = 0.0013.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "P(Ana OR Bea above 185) = P(Ana above 185) + P(Bea above 185) - P(Ana above 185)*P(Bea above 185) = \r\n" );
document.write( "\r\n" );
document.write( "                               = 0.1587 + 0.0013 - 0.1587 *0.0013 = 0.1598.   ANSWER to question A)\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved (correctly).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );