Suppose that an Ipad has an average lifespan of 5 years. We are interested in the life of the load. What is the probability that an Ipad would last more than 7 years?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To determine the probability that an iPad lasts more than 7 years, assuming an average lifespan of 5 years, we typically model the lifetime of electronic devices using an exponential distribution<\/strong>. The probability density function (PDF) of an exponentially distributed random variable ( T ) with mean ( \\lambda ) is:<\/p>\n\n\n\n [ where ( \\lambda ) is the mean lifespan (in this case, 5 years). The cumulative distribution function (CDF), which gives the probability that the iPad lasts at most<\/strong> ( t ) years, is:<\/p>\n\n\n\n [ We want to find the probability that an iPad lasts more than 7 years<\/strong>, which is given by:<\/p>\n\n\n\n [ Now, calculating:<\/p>\n\n\n\n [ The exponential distribution is commonly used for modeling the lifespan of electronic devices due to its memoryless property<\/strong>, meaning that the probability of survival beyond a certain time is independent of how long the device has already lasted.<\/p>\n\n\n\n In this case, the mean lifespan<\/strong> of an iPad is 5 years. The exponential model assumes that failure happens at a constant rate over time, making it a reasonable approximation for devices that degrade due to wear and tear.<\/p>\n\n\n\n By computing ( P(T > 7) = e^{-7\/5} \\approx 0.2466 ), we find that there is approximately a 24.66% chance that an iPad lasts more than 7 years<\/strong>. This suggests that while some iPads will last significantly longer than expected, most will fail within or around the 5-year mark.<\/p>\n\n\n\n This model can also be used for reliability analysis of other electronic devices, helping consumers and manufacturers estimate product longevity.<\/p>\n","protected":false},"excerpt":{"rendered":" Suppose that an Ipad has an average lifespan of 5 years. We are interested in the life of the load. What is the probability that an Ipad would last more than 7 years? The Correct Answer and Explanation is : To determine the probability that an iPad lasts more than 7 years, assuming an average […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-187822","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187822","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=187822"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187822\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187822"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187822"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187822"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
f(t) = \\frac{1}{\\lambda} e^{-t\/\\lambda}, \\quad t \\geq 0
]<\/p>\n\n\n\n
P(T \\leq t) = 1 – e^{-t\/\\lambda}
]<\/p>\n\n\n\n
P(T > 7) = 1 – P(T \\leq 7) = e^{-7\/5}
]<\/p>\n\n\n\n
P(T > 7) = e^{-7\/5} = e^{-1.4} \\approx 0.2466
]<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n