{"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\/de\/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":{"_uag_custom_page_level_css":"","_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":["post-1304","product","type-product","status-publish","has-post-thumbnail","product_cat-ornament","first","instock","shipping-taxable","product-type-simple","entry","content-bg","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":"","spectra_custom_meta":{"rank_math_internal_links_processed":["1","1","1","1","1","1","1"],"_tax_status":["taxable"],"_tax_class":[""],"_manage_stock":["no"],"_backorders":["no"],"_sold_individually":["no"],"_virtual":["no"],"_downloadable":["no"],"_product_image_gallery":["1305,1310,1308,1311"],"_download_limit":["-1"],"_download_expiry":["-1"],"_thumbnail_id":["1307"],"_stock":[null],"_stock_status":["instock"],"_wc_average_rating":["0"],"_wc_review_count":["0"],"_product_version":["10.1.2"],"_price":[""],"rank_math_seo_score":["61"],"_wp_page_template":["default"],"rank_math_primary_product_brand":["0"],"rank_math_primary_product_cat":["84"],"_kad_post_transparent":["default"],"_kad_post_layout":["default"],"_kad_post_content_style":["default"],"_kad_post_vertical_padding":["default"],"rank_math_title":["Galton board normal distribution model ornament"],"rank_math_focus_keyword":["Galton board"],"_wpb_gqb_disable":["no"],"_edit_lock":["1766732780:1"],"_edit_last":["1"],"max_price":["80"],"min_price":["55"],"total_sales":["0"],"_sale_price":[""],"litespeed_vpi_list":["a:9:{i:0;s:29:\"cropped-welleltron_logo-1.png\";i:1;s:26:\"Galton-board_2-600x600.png\";i:2;s:24:\"Galton-board-600x600.png\";i:3;s:26:\"Galton-board_2-100x100.png\";i:4;s:24:\"Galton-board-100x100.png\";i:5;s:26:\"Galton-board_6-100x100.png\";i:6;s:22:\"Galton-board_3-100x100\";i:7;s:26:\"Galton-board_7-100x100.png\";i:8;s:9:\"es_ES.png\";}"],"_uag_css_file_name":["uag-css-1304.css"],"_uag_page_assets":["a:9:{s:3:\"css\";s:260:\".uag-blocks-common-selector{z-index:var(--z-index-desktop) !important}@media(max-width: 976px){.uag-blocks-common-selector{z-index:var(--z-index-tablet) !important}}@media(max-width: 767px){.uag-blocks-common-selector{z-index:var(--z-index-mobile) !important}}\";s:2:\"js\";s:0:\"\";s:18:\"current_block_list\";a:26:{i:0;s:12:\"core\/heading\";i:1;s:9:\"core\/list\";i:2;s:14:\"core\/list-item\";i:3;s:9:\"core\/code\";i:4;s:10:\"core\/group\";i:5;s:12:\"core\/columns\";i:6;s:14:\"core\/tag-cloud\";i:7;s:17:\"core\/social-links\";i:8;s:10:\"core\/video\";i:9;s:15:\"core\/media-text\";i:10;s:14:\"core\/paragraph\";i:11;s:10:\"core\/audio\";i:12;s:10:\"core\/image\";i:13;s:10:\"core\/verse\";i:14;s:14:\"core\/pullquote\";i:15;s:17:\"core\/preformatted\";i:16;s:12:\"core\/details\";i:17;s:14:\"core\/page-list\";i:18;s:18:\"core\/legacy-widget\";i:20;s:16:\"core\/social-link\";i:21;s:12:\"kadence\/form\";i:22;s:14:\"kadence\/search\";i:23;s:16:\"kadence\/iconlist\";i:24;s:16:\"kadence\/listitem\";i:25;s:12:\"kadence\/icon\";i:26;s:19:\"kadence\/single-icon\";}s:8:\"uag_flag\";b:0;s:11:\"uag_version\";s:10:\"1793971938\";s:6:\"gfonts\";a:0:{}s:10:\"gfonts_url\";s:0:\"\";s:12:\"gfonts_files\";a:0:{}s:14:\"uag_faq_layout\";b:0;}"],"_elementor_page_assets":["a:0:{}"]},"uagb_featured_image_src":{"full":["https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_2.png",850,850,false],"thumbnail":["https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_2-150x150.png",150,150,true],"medium":["https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_2-300x300.png",300,300,true],"medium_large":["https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_2-768x768.png",768,768,true],"large":["https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_2.png",850,850,false],"1536x1536":["https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_2.png",850,850,false],"2048x2048":["https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_2.png",850,850,false],"trp-custom-language-flag":["https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_2.png",12,12,false],"woocommerce_thumbnail":["https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_2-300x300.png",300,300,true],"woocommerce_single":["https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_2-600x600.png",600,600,true],"woocommerce_gallery_thumbnail":["https:\/\/welleltron.com\/wp-content\/uploads\/2025\/12\/Galton-board_2-100x100.png",100,100,true]},"uagb_author_info":{"display_name":"lucaismilelove@gmail.com","author_link":"https:\/\/welleltron.com\/de\/blog\/author\/"},"uagb_comment_info":0,"uagb_excerpt":"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.","_links":{"self":[{"href":"https:\/\/welleltron.com\/de\/wp-json\/wp\/v2\/product\/1304","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/welleltron.com\/de\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/welleltron.com\/de\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/welleltron.com\/de\/wp-json\/wp\/v2\/media\/1307"}],"wp:attachment":[{"href":"https:\/\/welleltron.com\/de\/wp-json\/wp\/v2\/media?parent=1304"}],"wp:term":[{"taxonomy":"product_brand","embeddable":true,"href":"https:\/\/welleltron.com\/de\/wp-json\/wp\/v2\/product_brand?post=1304"},{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/welleltron.com\/de\/wp-json\/wp\/v2\/product_cat?post=1304"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/welleltron.com\/de\/wp-json\/wp\/v2\/product_tag?post=1304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}