{"id":263901,"date":"2025-07-21T09:52:01","date_gmt":"2025-07-21T09:52:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=263901"},"modified":"2025-07-21T09:52:03","modified_gmt":"2025-07-21T09:52:03","slug":"if-you-light-the-fuse-of-a-firecracker-the-time-it-will-take-to-explode-is-n3-2-1-22-seconds","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/if-you-light-the-fuse-of-a-firecracker-the-time-it-will-take-to-explode-is-n3-2-1-22-seconds\/","title":{"rendered":"If you light the fuse of a firecracker the time it will take to explode is N(3.2, 1.22) seconds"},"content":{"rendered":"\n<p>If you light the fuse of a firecracker the time it will take to explode is N(3.2, 1.22) seconds. What is the probability that a firecracker will take longer than 4.2 seconds to explode? Use 4 decimal places What is the probability that two firecrackers will take longer than 4.2 seconds to explode on average? Use 4 decimal places What is the probability that three firecrackers will take longer than 4.2 seconds to explode on average? Use 4 decimal places<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this, we will apply concepts from probability, specifically the <strong>normal distribution<\/strong>. The time it takes for a firecracker to explode follows a normal distribution with the following parameters:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mean (\u03bc) = 3.2 seconds<\/li>\n\n\n\n<li>Standard deviation (\u03c3) = 1.22 seconds<\/li>\n<\/ul>\n\n\n\n<p>We will use the z-score formula to find the probabilities:z=x\u2212\u03bc\u03c3z = \\frac{x &#8211; \\mu}{\\sigma}z=\u03c3x\u2212\u03bc\u200b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>xxx is the value we are comparing to (in this case, 4.2 seconds),<\/li>\n\n\n\n<li>\u03bc\\mu\u03bc is the mean (3.2 seconds),<\/li>\n\n\n\n<li>\u03c3\\sigma\u03c3 is the standard deviation (1.22 seconds).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">1. <strong>Probability for one firecracker<\/strong><\/h3>\n\n\n\n<p>We are interested in finding the probability that a firecracker will take <strong>longer than 4.2 seconds<\/strong> to explode.<\/p>\n\n\n\n<p>First, we calculate the z-score:z=4.2\u22123.21.22=1.01.22\u22480.8197z = \\frac{4.2 &#8211; 3.2}{1.22} = \\frac{1.0}{1.22} \\approx 0.8197z=1.224.2\u22123.2\u200b=1.221.0\u200b\u22480.8197<\/p>\n\n\n\n<p>Next, we use a z-table or a standard normal distribution calculator to find the cumulative probability for a z-score of 0.8197. This gives:P(Z&lt;0.8197)\u22480.7939P(Z &lt; 0.8197) \\approx 0.7939P(Z&lt;0.8197)\u22480.7939<\/p>\n\n\n\n<p>Now, since we want the probability that the firecracker will take <strong>longer<\/strong> than 4.2 seconds, we subtract this cumulative probability from 1:P(X&gt;4.2)=1\u22120.7939=0.2061P(X &gt; 4.2) = 1 &#8211; 0.7939 = 0.2061P(X&gt;4.2)=1\u22120.7939=0.2061<\/p>\n\n\n\n<p>So, the probability that a firecracker will take longer than 4.2 seconds to explode is approximately <strong>0.2061<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. <strong>Probability for two firecrackers<\/strong><\/h3>\n\n\n\n<p>For two firecrackers, we are looking for the probability that <strong>both<\/strong> will take longer than 4.2 seconds to explode on average. The key assumption here is that the times are independent, so the probability for each firecracker is independent.<\/p>\n\n\n\n<p>The probability for each firecracker to take longer than 4.2 seconds is <strong>0.2061<\/strong>, and for two firecrackers, we multiply this probability by itself:P(both)=0.2061\u00d70.2061=0.0425P(\\text{both}) = 0.2061 \\times 0.2061 = 0.0425P(both)=0.2061\u00d70.2061=0.0425<\/p>\n\n\n\n<p>So, the probability that both firecrackers will take longer than 4.2 seconds to explode on average is approximately <strong>0.0425<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. <strong>Probability for three firecrackers<\/strong><\/h3>\n\n\n\n<p>For three firecrackers, the same logic applies, and we simply multiply the individual probability three times:P(all&nbsp;three)=0.2061\u00d70.2061\u00d70.2061=0.0088P(\\text{all three}) = 0.2061 \\times 0.2061 \\times 0.2061 = 0.0088P(all&nbsp;three)=0.2061\u00d70.2061\u00d70.2061=0.0088<\/p>\n\n\n\n<p>So, the probability that all three firecrackers will take longer than 4.2 seconds to explode on average is approximately <strong>0.0088<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Probability that one firecracker will take longer than 4.2 seconds: <strong>0.2061<\/strong><\/li>\n\n\n\n<li>Probability that two firecrackers will take longer than 4.2 seconds to explode on average: <strong>0.0425<\/strong><\/li>\n\n\n\n<li>Probability that three firecrackers will take longer than 4.2 seconds to explode on average: <strong>0.0088<\/strong><\/li>\n<\/ul>\n\n\n\n<p>These probabilities make sense because as the number of firecrackers increases, the likelihood that <strong>all<\/strong> will take longer than 4.2 seconds decreases exponentially.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1345.jpeg\" alt=\"\" class=\"wp-image-263902\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>If you light the fuse of a firecracker the time it will take to explode is N(3.2, 1.22) seconds. What is the probability that a firecracker will take longer than 4.2 seconds to explode? Use 4 decimal places What is the probability that two firecrackers will take longer than 4.2 seconds to explode on average? [&hellip;]<\/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-263901","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/263901","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=263901"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/263901\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=263901"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=263901"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=263901"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}