In 25 polcapitas contemptions of sofiat drinks in Country A was reported to be 18.26 gallons. Assume that per capita consumption of soft drinks in Country A is approximately normally distributed, with a mean of 18.26 gallons and a standard deviation of 4 gallons. What is the probibility that Someone in Country A consumed more than 13 gallons of soft drinks in 2008?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The probability that someone in Country A consumed more than 13 gallons of soft drinks in 2008 is approximately 90.57%<\/strong>.<\/p>\n\n\n\n To solve this problem, we assume that the per capita consumption of soft drinks follows a normal distribution<\/strong> with a given mean (\u03bc) = 18.26 gallons<\/strong> and standard deviation (\u03c3) = 4 gallons<\/strong>.<\/p>\n\n\n\n We need to determine the probability that an individual consumed more than 13 gallons<\/strong>. This is done by calculating the Z-score<\/strong>, which standardizes the given consumption value:<\/p>\n\n\n\n [ Substituting the values:<\/p>\n\n\n\n [ The Z-score tells us how many standard deviations the value is from the mean. Next, we use the cumulative distribution function (CDF)<\/strong> of the standard normal distribution to find the probability that someone consumed less than 13 gallons<\/strong>:<\/p>\n\n\n\n [ Since we need the probability of consuming more than 13 gallons<\/strong>, we subtract this value from 1:<\/p>\n\n\n\n [ Thus, the probability that a randomly selected person in Country A consumed more than 13 gallons of soft drinks in 2008 is 90.57%<\/strong>.<\/p>\n\n\n\n This result suggests that most people (about 90.57%) in Country A consume more than 13 gallons<\/strong> of soft drinks annually. Since 13 gallons is below the mean (18.26 gallons), it makes sense that a large proportion of the population would exceed this amount. The normal distribution allows us to estimate how consumption is spread among individuals.<\/p>\n","protected":false},"excerpt":{"rendered":" In 25 polcapitas contemptions of sofiat drinks in Country A was reported to be 18.26 gallons. Assume that per capita consumption of soft drinks in Country A is approximately normally distributed, with a mean of 18.26 gallons and a standard deviation of 4 gallons. What is the probibility that Someone in Country A consumed more […]<\/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-191017","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191017","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=191017"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191017\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=191017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=191017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=191017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
Z = \\frac{X – \\mu}{\\sigma}
]<\/p>\n\n\n\n
Z = \\frac{13 – 18.26}{4} = \\frac{-5.26}{4} = -1.315
]<\/p>\n\n\n\n
P(X < 13) = P(Z < -1.315) \\approx 0.0943
]<\/p>\n\n\n\n
P(X > 13) = 1 – 0.0943 = 0.9057
]<\/p>\n\n\n\nInterpretation:<\/h3>\n\n\n\n