{"id":225,"date":"2024-05-06T11:21:37","date_gmt":"2024-05-06T11:21:37","guid":{"rendered":"https:\/\/casestudyhelp.net\/questions\/?p=225"},"modified":"2024-05-06T11:21:37","modified_gmt":"2024-05-06T11:21:37","slug":"which-of-the-following-probabilities-is-the-greatest-for-a-standard-normal-distribution","status":"publish","type":"post","link":"https:\/\/casestudyhelp.net\/questions\/which-of-the-following-probabilities-is-the-greatest-for-a-standard-normal-distribution\/","title":{"rendered":"Which of the Following Probabilities is the Greatest for a Standard Normal Distribution?"},"content":{"rendered":"<p style=\"background: white;\">Which of the Following Probabilities is the Greatest for a Standard Normal Distribution?<\/p>\n<p style=\"background: white;\"><span style=\"font-size: 13.5pt; font-family: 'Segoe UI','sans-serif'; color: black;\"><strong>A.<\/strong> p(-1.5\u2264z\u2264-0.5)<\/span><\/p>\n<p style=\"background: white; margin-block: 1.5rem 0px; max-width: var(--wp--style--global--content-size);\"><span style=\"font-size: 13.5pt; font-family: 'Segoe UI','sans-serif'; color: black;\"><strong>B.<\/strong> p(-0.5\u2264z\u22640.5)<\/span><\/p>\n<p style=\"background: white; margin-block: 1.5rem 0px; max-width: var(--wp--style--global--content-size);\"><span style=\"font-size: 13.5pt; font-family: 'Segoe UI','sans-serif'; color: black;\"><strong>C.<\/strong> p(0.5\u2264z\u22641.5)<\/span><\/p>\n<p style=\"background: white; margin-block: 1.5rem 0px; max-width: var(--wp--style--global--content-size);\"><span style=\"font-size: 13.5pt; font-family: 'Segoe UI','sans-serif'; color: black;\"><strong>D.<\/strong> p(1.5\u2264z\u22642.5)<\/span><\/p>\n<h3 style=\"background: white;\"><strong>Answer:- B. p(-0.5\u2264z\u22640.5)<\/strong><\/h3>\n<p class=\"western\" style=\"background: white; margin-block: 1.5rem 0px; max-width: var(--wp--style--global--content-size);\"><span style=\"font-size: 13.5pt; font-family: 'Segoe UI','sans-serif'; color: black;\">A standard normal distribution has mean 0 and a variance of one. It is about 68% of the area under normal curve lies within one standard deviation from mean value (between negative and positive). Probability decreases with the increase in standard deviation from mean.<\/span><\/p>\n<p class=\"western\" style=\"background: white;\"><span style=\"font-size: 13.5pt; font-family: 'Segoe UI','sans-serif'; color: black;\">Option B mentions the range around the mean of +\/- 0.5 standard deviations, which is the least supportive measure for failure mode and effect analysis to differentiate between acceptable design or process variations from failures. This has the largest proportion of area under the curve compared to all other wider intervals taken in options A, C and D.<\/span><\/p>\n<p class=\"western\" style=\"background: white; margin-block: 1.5rem 0px; max-width: var(--wp--style--global--content-size);\"><span style=\"font-size: 13.5pt; font-family: 'Segoe UI','sans-serif'; color: black;\">In particular, 68% of the region lies between -1 to +0 standard deviation away from mean. Within a narrower zone of -0.5 to 0. The other three options, A, C and D have wider intervals more removed from the mean so they will be lower probabilities.<\/span><\/p>\n<p class=\"western\" style=\"background: white; margin-block: 1.5rem 0px; max-width: var(--wp--style--global--content-size);\"><span style=\"font-size: 13.5pt; font-family: 'Segoe UI','sans-serif'; color: black;\">Thus, p(-0.5\u2264z\u22640.5) represents the largest probability for a standard normal distribution compared by all other possibilities The closest interval to the mean captures almost all of the total area under the normal curve .<\/span><\/p>\n<h2><strong>Get Assignment Answers Related to all Subjects in Your Academic<\/strong><\/h2>\n<p style=\"text-align: center;\"><a href=\"https:\/\/casestudyhelp.net\/order-now.php\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1378 size-full\" src=\"https:\/\/casestudyhelp.net\/questions\/wp-content\/uploads\/2024\/05\/Yes-We-Can-help-You.webp\" alt=\"Get Homework Answers\" width=\"800\" height=\"180\" \/><\/a><\/p>\n<blockquote><p>Looking for <span style=\"font-size: 13.5pt; font-family: 'Segoe UI','sans-serif'; color: black;\">normal distribution for <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/casestudyhelp.net\/au\/\"><strong>Assignment Help<\/strong><\/a><\/span>? If yes Get perfect answer of normal distribution from <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/casestudyhelp.net\/experts\/\"><strong>Assignment experts<\/strong><\/a><\/span> at casestudyhelp.net. And 100% non-plagiarism free work with on-time delivery. place your order.<\/span><\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Which of the Following Probabilities is the Greatest for a Standard Normal Distribution? 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