{"id":8370,"date":"2024-04-15T02:59:30","date_gmt":"2024-04-15T02:59:30","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=8370"},"modified":"2024-04-15T02:59:30","modified_gmt":"2024-04-15T02:59:30","slug":"if-a-is-the-optimistic-time-b-is-the-pessimistic-time-and-m-is-most-likely-time-of-an-activity-the-expected-time-of-the-activity-is-a-fractexta-textm-textb6-b","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-a-is-the-optimistic-time-b-is-the-pessimistic-time-and-m-is-most-likely-time-of-an-activity-the-expected-time-of-the-activity-is-a-fractexta-textm-textb6-b\/","title":{"rendered":"If a is the optimistic time, b is the pessimistic time and m is most likely time of an activity, the expected time of the activity, is A. $$\\frac{{{\\text{a}} + {\\text{m}} + {\\text{b}}}}{6}$$ B. $$\\frac{{{\\text{a}} + 2{\\text{m}} + {\\text{b}}}}{6}$$ C. $$\\frac{{{\\text{a}} + 4{\\text{m}} + {\\text{b}}}}{6}$$ D. $$\\frac{{{\\text{a}} + 5{\\text{m}} + {\\text{b}}}}{6}$$"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a99085b5754c\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    $$\frac{{{\text{a}} + {\text{m}} + {\text{b}}}}{6}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"true\">\r\n                    $$\frac{{{\text{a}} + 2{\text{m}} + {\text{b}}}}{6}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    $$\frac{{{\text{a}} + 4{\text{m}} + {\text{b}}}}{6}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    $$\frac{{{\text{a}} + 5{\text{m}} + {\text{b}}}}{6}$$                <\/div>\r\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is $\\frac{{{\\text{a}} + 4{\\text{m}} + {\\text{b}}}}{6}$.<\/p>\n<p>The expected time of an activity is the weighted average of the optimistic time, the most likely time, and the pessimistic time. The weights are 1\/6, 4\/6, and 1\/6, respectively. This is because the optimistic time is the least likely time to occur, the most likely time is the most likely time to occur, and the pessimistic time is the most likely time to occur.<\/p>\n<p>The formula for the expected time of an activity is:<\/p>\n<p>$E = \\frac{{{\\text{a}} + 4{\\text{m}} + {\\text{b}}}}{6}$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$a$ is the optimistic time<\/li>\n<li>$m$ is the most likely time<\/li>\n<li>$b$ is the pessimistic time<\/li>\n<\/ul>\n<p>For example, if the optimistic time for an activity is 1 day, the <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div> most likely time is 3 days, and the pessimistic time is 5 days, then the expected time of the activity is:<\/p>\n<p>$E = \\frac{{{\\text{a}} + 4{\\text{m}} + {\\text{b}}}}{6} = \\frac{{1 + 4 \\times 3 + 5}}{6} = 3$ days<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[655],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>If a is the optimistic time, b is the pessimistic time and m is most likely time of an activity, the expected time of the activity, is A. $$\\frac{{{\\text{a}} + {\\text{m}} + {\\text{b}}}}{6}$$ B. $$\\frac{{{\\text{a}} + 2{\\text{m}} + {\\text{b}}}}{6}$$ C. $$\\frac{{{\\text{a}} + 4{\\text{m}} + {\\text{b}}}}{6}$$ D. $$\\frac{{{\\text{a}} + 5{\\text{m}} + {\\text{b}}}}{6}$$<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/if-a-is-the-optimistic-time-b-is-the-pessimistic-time-and-m-is-most-likely-time-of-an-activity-the-expected-time-of-the-activity-is-a-fractexta-textm-textb6-b\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If a is the optimistic time, b is the pessimistic time and m is most likely time of an activity, the expected time of the activity, is A. $$\\frac{{{\\text{a}} + {\\text{m}} + {\\text{b}}}}{6}$$ B. $$\\frac{{{\\text{a}} + 2{\\text{m}} + {\\text{b}}}}{6}$$ C. $$\\frac{{{\\text{a}} + 4{\\text{m}} + {\\text{b}}}}{6}$$ D. $$\\frac{{{\\text{a}} + 5{\\text{m}} + {\\text{b}}}}{6}$$\" \/>\n<meta property=\"og:description\" content=\"Subscribe on YouTube\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-a-is-the-optimistic-time-b-is-the-pessimistic-time-and-m-is-most-likely-time-of-an-activity-the-expected-time-of-the-activity-is-a-fractexta-textm-textb6-b\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T02:59:30+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" 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activity, is A. $$\\frac{{{\\text{a}} + {\\text{m}} + {\\text{b}}}}{6}$$ B. $$\\frac{{{\\text{a}} + 2{\\text{m}} + {\\text{b}}}}{6}$$ C. $$\\frac{{{\\text{a}} + 4{\\text{m}} + {\\text{b}}}}{6}$$ D. $$\\frac{{{\\text{a}} + 5{\\text{m}} + {\\text{b}}}}{6}$$","og_description":"Subscribe on YouTube","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-a-is-the-optimistic-time-b-is-the-pessimistic-time-and-m-is-most-likely-time-of-an-activity-the-expected-time-of-the-activity-is-a-fractexta-textm-textb6-b\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T02:59:30+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 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