{"id":196192,"date":"2025-03-03T17:30:13","date_gmt":"2025-03-03T17:30:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=196192"},"modified":"2025-03-03T17:30:16","modified_gmt":"2025-03-03T17:30:16","slug":"assuming-that-the-change-in-daily-closing-prices-for-stocks-on-the-new-york-stock-exchange-is-a-random-variable-that-is-normally-distributed-with-a-mean-of-35-and-a-standard-deviation-of-33-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/03\/assuming-that-the-change-in-daily-closing-prices-for-stocks-on-the-new-york-stock-exchange-is-a-random-variable-that-is-normally-distributed-with-a-mean-of-35-and-a-standard-deviation-of-33-2\/","title":{"rendered":"Assuming that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $.35 and a standard deviation of $.33"},"content":{"rendered":"\n

Assuming that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $.35 and a standard deviation of $.33. Based on this information, what is the probability that a randomly selected stock will close up $.75 or more?<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The probability that a randomly selected stock will close up by $0.75 or more is 0.1127<\/strong> (or 11.27%<\/strong>).<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

The problem states that the daily changes in stock closing prices on the New York Stock Exchange follow a normal distribution with:<\/p>\n\n\n\n

    \n
  • Mean (\u03bc\\mu) = $0.35<\/strong><\/li>\n\n\n\n
  • Standard deviation (\u03c3\\sigma) = $0.33<\/strong><\/li>\n\n\n\n
  • Target value (XX) = $0.75<\/strong><\/li>\n<\/ul>\n\n\n\n

    To find the probability P(X\u22650.75)P(X \\geq 0.75), we calculate the Z-score<\/strong>: Z=X\u2212\u03bc\u03c3=0.75\u22120.350.33=0.400.33\u22481.21Z = \\frac{X – \\mu}{\\sigma} = \\frac{0.75 – 0.35}{0.33} = \\frac{0.40}{0.33} \\approx 1.21<\/p>\n\n\n\n

    Using the standard normal table, the cumulative probability for Z=1.21Z = 1.21 is 0.8873<\/strong>. Since we need P(X\u22650.75)P(X \\geq 0.75), we take the complement: P(X\u22650.75)=1\u2212P(Z\u22641.21)=1\u22120.8873=0.1127P(X \\geq 0.75) = 1 – P(Z \\leq 1.21) = 1 – 0.8873 = 0.1127<\/p>\n\n\n\n

    This means there is an 11.27% chance<\/strong> that a randomly selected stock will have a closing price increase of at least $0.75.<\/p>\n\n\n\n

    Interpretation:<\/h3>\n\n\n\n
      \n
    • Most stock price changes will be close to the mean ($0.35).<\/li>\n\n\n\n
    • The probability of a price increase of $0.75 or more is relatively low<\/strong>.<\/li>\n\n\n\n
    • The probability is visualized in the normal distribution graph<\/strong>, where the shaded red area represents the portion of stocks closing above $0.75.<\/li>\n<\/ul>\n\n\n\n

      This result can help investors understand the likelihood of significant stock price movements based on historical volatility.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Assuming that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $.35 and a standard deviation of $.33. Based on this information, what is the probability that a randomly selected stock will close up $.75 or more? The […]<\/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-196192","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196192","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=196192"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196192\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}