{"id":220267,"date":"2025-05-28T05:15:41","date_gmt":"2025-05-28T05:15:41","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=220267"},"modified":"2025-05-28T05:15:44","modified_gmt":"2025-05-28T05:15:44","slug":"assume-that-when-human-resource-managers-are-randomly-selected-52-say-job-applicants-should-follow-up-within-two-weeks","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/28\/assume-that-when-human-resource-managers-are-randomly-selected-52-say-job-applicants-should-follow-up-within-two-weeks\/","title":{"rendered":"Assume that when human resource managers are randomly selected, 52% say job applicants should follow up within two weeks."},"content":{"rendered":"\n

Assume that when human resource managers are randomly selected, 52% say job applicants should follow up within two weeks. If 5 human resource managers are randomly selected, find the probability that at least 3 of them say job applicants should follow up within two weeks.<\/p>\n\n\n\n

T he Correct Answer and Explanation is :<\/mark><\/strong><\/p>\n\n\n\n

To solve this problem, we use the binomial probability distribution<\/strong>, as we are dealing with a fixed number of independent trials (5 HR managers), each with only two possible outcomes (say “yes” or “no” to following up within two weeks).<\/p>\n\n\n\n

Given:<\/h3>\n\n\n\n
    \n
  • Probability of success (saying “yes”) p=0.52p = 0.52<\/li>\n\n\n\n
  • Number of trials n=5n = 5<\/li>\n\n\n\n
  • We want the probability that at least 3<\/strong> say yes: P(X\u22653)P(X \\geq 3)<\/li>\n\n\n\n
  • This is: P(X\u22653)=P(X=3)+P(X=4)+P(X=5)P(X \\geq 3) = P(X = 3) + P(X = 4) + P(X = 5)<\/li>\n<\/ul>\n\n\n\n

    We use the binomial probability formula: P(X=k)=(nk)pk(1\u2212p)n\u2212kP(X = k) = \\binom{n}{k} p^k (1 – p)^{n – k}<\/p>\n\n\n\n

    Let\u2019s compute:<\/p>\n\n\n\n

      \n
    1. P(X = 3)<\/strong>:<\/li>\n<\/ol>\n\n\n\n

      (53)(0.52)3(0.48)2=10\u00d70.140608\u00d70.2304\u22480.324\\binom{5}{3} (0.52)^3 (0.48)^2 = 10 \\times 0.140608 \\times 0.2304 \\approx 0.324<\/p>\n\n\n\n

        \n
      1. P(X = 4)<\/strong>:<\/li>\n<\/ol>\n\n\n\n

        (54)(0.52)4(0.48)1=5\u00d70.073725\u00d70.48\u22480.177\\binom{5}{4} (0.52)^4 (0.48)^1 = 5 \\times 0.073725 \\times 0.48 \\approx 0.177<\/p>\n\n\n\n

          \n
        1. P(X = 5)<\/strong>:<\/li>\n<\/ol>\n\n\n\n

          (55)(0.52)5(0.48)0=1\u00d70.038337\u00d71=0.038\\binom{5}{5} (0.52)^5 (0.48)^0 = 1 \\times 0.038337 \\times 1 = 0.038<\/p>\n\n\n\n

          Add them up:<\/h3>\n\n\n\n

          P(X\u22653)\u22480.324+0.177+0.038=0.539P(X \\geq 3) \\approx 0.324 + 0.177 + 0.038 = \\boxed{0.539}<\/p>\n\n\n\n

          \n\n\n\n

          Explanation<\/strong><\/h3>\n\n\n\n

          This problem involves calculating the probability that at least 3 out of 5 randomly selected human resource (HR) managers believe job applicants should follow up within two weeks. Since we are repeating the same trial (asking an HR manager) a fixed number of times (5), and each trial has only two possible outcomes (either they say \u201cyes\u201d or they don\u2019t), the binomial distribution<\/strong> is appropriate.<\/p>\n\n\n\n

          The binomial distribution is used to model the number of successes in a fixed number of independent trials, each with the same probability of success. Here, a \u201csuccess\u201d is an HR manager saying that applicants should follow up within two weeks, and the given success probability is 52% or 0.52.<\/p>\n\n\n\n

          We are asked to find the probability that at least 3<\/strong> out of 5 HR managers say \u201cyes.\u201d This is equivalent to finding the sum of the probabilities of exactly 3, 4, or 5 managers saying \u201cyes.\u201d We calculate each of these probabilities using the binomial probability formula<\/strong>: P(X=k)=(nk)pk(1\u2212p)n\u2212kP(X = k) = \\binom{n}{k} p^k (1 – p)^{n – k}<\/p>\n\n\n\n

          This formula calculates the probability of getting exactly kk successes in nn trials, with a success probability pp. We compute the individual probabilities for 3, 4, and 5 successes and then add them up. The result, approximately 0.539<\/strong>, indicates there is about a 53.9% chance that at least three of the five HR managers will recommend following up within two weeks.<\/p>\n\n\n\n

          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

          Assume that when human resource managers are randomly selected, 52% say job applicants should follow up within two weeks. If 5 human resource managers are randomly selected, find the probability that at least 3 of them say job applicants should follow up within two weeks. T he Correct Answer and Explanation is : To solve […]<\/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-220267","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220267","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=220267"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220267\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=220267"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=220267"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=220267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}