document.write( "Question 1200126: A cement truck delivers mixed cement to a large construction site. Let x represent the cycle time in minutes for the truck to leave the construction site, go back to the cement plant, fill up, and return to the construction site with another load of cement. From past experience, it is known that the mean cycle time is 𝜇 = 48 minutes with 𝜎 = 18 minutes. The x distribution is approximately normal.
\n" ); document.write( "(a) What is the probability that the cycle time will exceed 60 minutes, given that it has exceeded 50 minutes? (Round your answer to four decimal places.)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(b) What is the probability that the cycle time will exceed 55 minutes, given that it has exceeded 40 minutes? (Round your answer to four decimal places.)
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #834232 by ikleyn(52946)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "A cement truck delivers mixed cement to a large construction site.
\n" ); document.write( "Let x represent the cycle time in minutes for the truck to leave the construction site,
\n" ); document.write( "go back to the cement plant, fill up, and return to the construction site
\n" ); document.write( "with another load of cement. From past experience, it is known that the mean cycle time
\n" ); document.write( "is 𝜇 = 48 minutes with 𝜎 = 18 minutes. The x distribution is approximately normal.\r
\n" ); document.write( "\n" ); document.write( "(a) What is the probability that the cycle time will exceed 60 minutes,
\n" ); document.write( "given that it has exceeded 50 minutes? (Round your answer to four decimal places.)\r
\n" ); document.write( "\n" ); document.write( "(b) What is the probability that the cycle time will exceed 55 minutes,
\n" ); document.write( "given that it has exceeded 40 minutes? (Round your answer to four decimal places.)
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        In this my post,  I will solve and answer question  (a),  ONLY.\r
\n" ); document.write( "\n" ); document.write( "        I will leave question  (b)  to you,  because it is a  TWIN  to question  (a)\r
\n" ); document.write( "\n" ); document.write( "        and,  therefore,  I expect that it will be easy to you to solve it on your own,\r
\n" ); document.write( "\n" ); document.write( "        having a  TEMPLATE  in front of you.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        So, trace my solution for question  (a)  very attentively.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "This question is about conditional probability.\r\n" );
document.write( "\r\n" );
document.write( "We have an event A = { x > 60 } and an event B = { x > 50 }.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "They want you calculate the conditional probability P(A | B), which reads \" P of A given B\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This conditional probability is the ratio  \"P%28A_and_B%29%2FP%28B%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Here P(A and B) is the probability of the intersection (A and B).\r\n" );
document.write( "\r\n" );
document.write( "In this problem, OBVIOUSLY, event A is a part of the event B: indeed, if x > 60, then x > 50.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, P(A and B) = P(A)    <<<---=== exactly because A is a smaller part of B.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, our conditional probability  P(A | B) is the ratio  P(A | B) = \"P%28A%29%2FP%28B%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    +---------------------------------------------------------------------+\r\n" );
document.write( "    |    As soon as we got this understanding, we solved more than half   |\r\n" );
document.write( "    |         of the problem, and the rest is just a technique.           |\r\n" );
document.write( "    +---------------------------------------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Mow,   P(A) = normalcdf(60, 9999, 48, 18)  (it is the area under the normal curve \r\n" );
document.write( "                                           on the right of the raw mark x=60),\r\n" );
document.write( "\r\n" );
document.write( "  so,  using your calculator, you get the value  P(A) = 0.2525.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next,  P(B) = normalcdf(50, 9999, 48, 18)  (it is the area under the normal curve \r\n" );
document.write( "                                           on the right of the raw mark x=50),\r\n" );
document.write( "\r\n" );
document.write( "  so,  using your calculator, you get the value  P(B) = 0.4558.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Finally, the desired conditional probability is  \r\n" );
document.write( "\r\n" );
document.write( "         P(A | B) = \"P%28A%29%2FP%28B%29\" = \"0.2525%2F0.4558\" = 0.5540  (rounded).    ANSWER\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Thus the part  (a)  of the problem is just solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now boldly go forward and solve part  (b)  in the same way.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "/////////////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you need to learn about using calculators to work with function normalcdf,\r
\n" ); document.write( "\n" ); document.write( "you can find all necessary instructions from this video-lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Normal Distribution:   Calculating Probabilities   {TI 84 Plus CE}
\n" ); document.write( "https://www.youtube.com/watch?v=IyEKEL9nm28\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "or from this textual description\r
\n" ); document.write( "\n" ); document.write( "https://cosmosweb.champlain.edu/people/stevens/WebTech/TIFiles/Chap6-TI-83.pdf\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Happy learning,  solving and calculating  ( ! )\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );