{"id":1304,"date":"2025-12-07T03:18:11","date_gmt":"2025-12-07T03:18:11","guid":{"rendered":"https:\/\/welleltron.com\/?post_type=product&#038;p=1304"},"modified":"2025-12-26T07:03:49","modified_gmt":"2025-12-26T07:03:49","slug":"galton-board-normal-distribution-model-ornament","status":"publish","type":"product","link":"https:\/\/welleltron.com\/fr\/ornament\/galton-board-normal-distribution-model-ornament\/","title":{"rendered":"Galton board normal distribution model ornament"},"content":{"rendered":"<div>Detailed Explanation of the\u00a0<span class=\"keywords_replace\">Galton board<\/span>\u00a0Normal Distribution Experiment Experimental Setup:<\/div>\n<div><strong>Vertical plate: I<\/strong>t has an opening at the top and multiple vertical collection grooves arranged at the bottom.<\/div>\n<div><\/div>\n<div><strong>Multi-layer nails:\u00a0<\/strong>The nails are arranged alternately, with one more nail on each layer than the upper one, forming a triangular layout. The small ball: Released from the top, it collides with the nail during its fall and eventually lands in a certain groove at the bottom.<\/div>\n<div><\/div>\n<div><strong>Experimental phenomenon:<\/strong><\/div>\n<div>The path of a single small ball is random and it may fall into any slot.<\/div>\n<div>After releasing a large number of small balls, the middle slot accumulates the most, while the number on both sides gradually decreases, forming a bell-shaped curve.<\/div>\n<div><\/div>\n<div><strong>Mathematical principle:<\/strong><\/div>\n<div><strong><span class=\"keywords_replace\">binomial distribution model<\/span><\/strong><strong>:<\/strong><\/div>\n<div>Each layer of nails represents an independent test. The probability p of each collision of the small ball to the left\/right is 0.5.<\/div>\n<div><\/div>\n<div><strong><span class=\"keywords_replace\">Dalton board<\/span>\u00a0<\/strong><strong>Application field:<\/strong><\/div>\n<div><strong>Probability education:\u00a0<\/strong>Visually demonstrate how random processes generate deterministic distributions.<\/div>\n<div><strong>Quality control:<\/strong>\u00a0Simulate the cumulative effect of production errors and explain the normal distribution phenomenon of product parameters.<\/div>\n<div><strong>Financial model:<\/strong>\u00a0By analogy with the random walk of asset prices, it provides physical intuition for the Black-Shulls option pricing model.<\/div>\n<div>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-1309\" src=\"https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_4-188x300.png\" alt=\"Galton Board 4\" width=\"639\" height=\"1019\" srcset=\"https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_4-188x300.png 188w, https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_4-643x1024.png 643w\" sizes=\"(max-width: 639px) 100vw, 639px\" \/><\/p>\n<\/div>\n<div><\/div>","protected":false},"excerpt":{"rendered":"<p>Galton board normal distribution model ornament is a decorative or educational display device that uses the random descent of small balls through a field of pegs to visually and physically demonstrate the Central Limit Theorem and the formation of a bell-shaped normal distribution curve.<\/p>","protected":false},"featured_media":1307,"template":"","meta":{"_kad_blocks_custom_css":"","_kad_blocks_head_custom_js":"","_kad_blocks_body_custom_js":"","_kad_blocks_footer_custom_js":"","_kad_post_transparent":"default","_kad_post_title":"","_kad_post_layout":"default","_kad_post_sidebar_id":"","_kad_post_content_style":"default","_kad_post_vertical_padding":"default","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false},"product_brand":[],"product_cat":[84],"product_tag":[],"class_list":{"0":"post-1304","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-ornament","8":"first","9":"instock","10":"shipping-taxable","11":"product-type-simple","12":"entry","13":"content-bg","14":"loop-entry"},"taxonomy_info":{"product_cat":[{"value":84,"label":"Ornament"}]},"featured_image_src_large":["https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_2.png",850,850,false],"author_info":[],"comment_info":"","_links":{"self":[{"href":"https:\/\/welleltron.com\/fr\/wp-json\/wp\/v2\/product\/1304","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/welleltron.com\/fr\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/welleltron.com\/fr\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/welleltron.com\/fr\/wp-json\/wp\/v2\/media\/1307"}],"wp:attachment":[{"href":"https:\/\/welleltron.com\/fr\/wp-json\/wp\/v2\/media?parent=1304"}],"wp:term":[{"taxonomy":"product_brand","embeddable":true,"href":"https:\/\/welleltron.com\/fr\/wp-json\/wp\/v2\/product_brand?post=1304"},{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/welleltron.com\/fr\/wp-json\/wp\/v2\/product_cat?post=1304"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/welleltron.com\/fr\/wp-json\/wp\/v2\/product_tag?post=1304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}