{"id":25890,"date":"2025-06-19T10:13:43","date_gmt":"2025-06-19T10:13:43","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25890"},"modified":"2025-06-19T10:16:30","modified_gmt":"2025-06-19T10:16:30","slug":"choose-the-statement-that-correctly-describes-a-normal-distribution-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/choose-the-statement-that-correctly-describes-a-normal-distribution-2\/","title":{"rendered":"Choose the statement that correctly describes a normal distribution"},"content":{"rendered":"\n<p>Choose the statement that correctly describes a normal distribution. A. The approximate percent of values lying within two standard deviations of the mean is 47.5% B. Approximately 68% of the values are greater than the mean value. C. Approximately 68% of the values lie within one standard deviation of the mean. D. The approximate percent of values lying within three standard deviations of the mean is 49.85%<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p><strong>Correct Answer: C. Approximately 68% of the values lie within one standard deviation of the mean.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words):<\/h3>\n\n\n\n<p>A <strong>normal distribution<\/strong>, also known as a <strong>Gaussian distribution<\/strong>, is a symmetrical, bell-shaped curve that describes how data is distributed around the mean (average). In a normal distribution, the mean, median, and mode are all equal and lie at the center of the curve. The spread of the distribution is measured by the <strong>standard deviation (\u03c3)<\/strong>, which tells us how much the values deviate from the mean.<\/p>\n\n\n\n<p>The <strong>Empirical Rule<\/strong>, also known as the <strong>68-95-99.7 Rule<\/strong>, is used to describe the percentage of data that falls within certain standard deviations from the mean in a normal distribution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Approximately 68%<\/strong> of the data values lie <strong>within one standard deviation<\/strong> of the mean (from \u03bc &#8211; \u03c3 to \u03bc + \u03c3). This supports <strong>Option C<\/strong>, making it the correct choice.<\/li>\n\n\n\n<li><strong>Approximately 95%<\/strong> of the data lie <strong>within two standard deviations<\/strong> of the mean (from \u03bc &#8211; 2\u03c3 to \u03bc + 2\u03c3), <strong>not 47.5%<\/strong> as stated in Option A.<\/li>\n\n\n\n<li><strong>Approximately 99.7%<\/strong> of the data fall <strong>within three standard deviations<\/strong> (from \u03bc &#8211; 3\u03c3 to \u03bc + 3\u03c3), <strong>not 49.85%<\/strong> as stated in Option D.<\/li>\n\n\n\n<li>Because the distribution is symmetrical, <strong>about 50% of the values lie above the mean<\/strong> and <strong>50% lie below<\/strong>. So, <strong>Option B is incorrect<\/strong> because only <strong>about 50%<\/strong>, not 68%, are greater than the mean.<\/li>\n<\/ul>\n\n\n\n<p>Understanding the properties of the normal distribution is essential in fields such as statistics, psychology, and economics because it provides a basis for making predictions and understanding variability in data. The 68% rule is especially helpful in quickly estimating probabilities and analyzing the reliability of measured data.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Choose the statement that correctly describes a normal distribution. A. The approximate percent of values lying within two standard deviations of the mean is 47.5% B. Approximately 68% of the values are greater than the mean value. C. Approximately 68% of the values lie within one standard deviation of the mean. D. The approximate percent [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-25890","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25890","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=25890"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25890\/revisions"}],"predecessor-version":[{"id":26088,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25890\/revisions\/26088"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25890"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25890"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25890"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}