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 Answer: Approximately 11.3%<\/p>\n\n\n\n Explanation: To solve this, we first convert the problem to the standard normal distribution by using the Z-score formula:<\/p>\n\n\n\n \u2003\u2003Z = (X \u2013 \u03bc) \/ \u03c3<\/p>\n\n\n\n Here, X is the value of interest ($0.75). Plugging in the values, we get:<\/p>\n\n\n\n \u2003\u2003Z = (0.75 \u2013 0.35) \/ 0.33 = 0.40 \/ 0.33 \u2248 1.21<\/p>\n\n\n\n This Z-score of approximately 1.21 tells us that $0.75 is about 1.21 standard deviations above the mean. The next step is to find the cumulative probability corresponding to Z = 1.21. Standard normal distribution tables or calculators show that P(Z < 1.21) is roughly 0.887. This cumulative probability represents the chance that a stock\u2019s daily change is less than $0.75.<\/p>\n\n\n\n Since we need the probability for stocks closing at $0.75 or more, we take the complement of this value:<\/p>\n\n\n\n \u2003\u2003P(X \u2265 0.75) = 1 \u2013 P(Z < 1.21) \u2248 1 \u2013 0.887 \u2248 0.113<\/p>\n\n\n\n Thus, there is about an 11.3% chance that a randomly selected stock will close up by $0.75 or more. This approach of converting to a standard normal variable is a fundamental technique in statistics, as it simplifies calculations by allowing the use of standardized tables or software. In summary, using the Z-score transformation and standard normal distribution properties, we determined that the probability is approximately 11.3%.<\/p>\n\n\n\n NYSE Stock Price Change Problem<\/p>\n\n\n\n Change in daily closing prices is normally distributed. Steps: Final Answer: ~11.3% 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-194681","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194681","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=194681"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194681\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194681"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194681"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194681"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
We begin with the assumption that the daily change in a stock\u2019s closing price is normally distributed with a mean (\u03bc) of $0.35 and a standard deviation (\u03c3) of $0.33. Our goal is to calculate the probability that a stock closes up by $0.75 or more, which can be written as P(X \u2265 0.75).<\/p>\n\n\n\n
Mean (\u03bc) = $0.35, Standard Deviation (\u03c3) = $0.33.
Question: What is the probability that a stock closes up $0.75 or more?<\/p>\n\n\n\n
1. Compute Z-score:
Z = (0.75 – 0.35) \/ 0.33 \u2248 1.21
2. Find cumulative probability P(Z < 1.21) \u2248 0.887.
3. Therefore, P(X \u2265 0.75) = 1 – 0.887 \u2248 0.113 or 11.3%.<\/p>\n\n\n\n
<\/p>\n","protected":false},"excerpt":{"rendered":"