{"id":191041,"date":"2025-02-14T05:33:02","date_gmt":"2025-02-14T05:33:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=191041"},"modified":"2025-02-14T05:33:05","modified_gmt":"2025-02-14T05:33:05","slug":"use-matlab-to-calculate-the-following-probabilities-and-percentiles-for-the-standard-normal-distribution","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/14\/use-matlab-to-calculate-the-following-probabilities-and-percentiles-for-the-standard-normal-distribution\/","title":{"rendered":"Use MATLAB\u00ae to calculate the following probabilities and percentiles for the standard normal distribution"},"content":{"rendered":"\n

part 1 Use MATLAB\u00ae to calculate the following probabilities and percentiles for the standard normal distribution:
a. ??(??=-2)
b. ??(??=1)
c. ??(-0.4=??=1.6)
d. The 5th percentile
e. The 75th percentile
f. The 99th percentile<\/p>\n\n\n\n

part 2<\/p>\n\n\n\n

Use MATLAB\u00ae to calculate the following probabilities and percentiles for the ??(75,8) distribution:
a. ??(??=70)
b. ??(??=73)
c. ??(75=??=85)
d. The 5th percentile
e. The 60th percentile
f. The 97th percentile<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

Here is the MATLAB code to compute the required probabilities and percentiles for both the standard normal distribution and the normal distribution with mean 75 and standard deviation 8.<\/p>\n\n\n\n

% Part 1: Standard Normal Distribution (mean = 0, std = 1)\nmu1 = 0;  % Mean of standard normal distribution\nsigma1 = 1; % Standard deviation of standard normal distribution\n\n% (a) P(X = -2) - Probability at a single point is always zero for continuous distributions\nPa = normpdf(-2, mu1, sigma1);\n\n% (b) P(X = 1)\nPb = normpdf(1, mu1, sigma1);\n\n% (c) P(-0.4 \u2264 X \u2264 1.6)\nPc = normcdf(1.6, mu1, sigma1) - normcdf(-0.4, mu1, sigma1);\n\n% (d) 5th percentile\nP5 = norminv(0.05, mu1, sigma1);\n\n% (e) 75th percentile\nP75 = norminv(0.75, mu1, sigma1);\n\n% (f) 99th percentile\nP99 = norminv(0.99, mu1, sigma1);\n\n% Display results for standard normal distribution\nfprintf('Standard Normal Distribution Results:\\n');\nfprintf('P(X = -2): %f\\n', Pa);\nfprintf('P(X = 1): %f\\n', Pb);\nfprintf('P(-0.4 \u2264 X \u2264 1.6): %f\\n', Pc);\nfprintf('5th percentile: %f\\n', P5);\nfprintf('75th percentile: %f\\n', P75);\nfprintf('99th percentile: %f\\n\\n', P99);\n\n% Part 2: Normal Distribution (mean = 75, std = 8)\nmu2 = 75;  % Mean\nsigma2 = 8; % Standard deviation\n\n% (a) P(X = 70)\nP70 = normpdf(70, mu2, sigma2);\n\n% (b) P(X = 73)\nP73 = normpdf(73, mu2, sigma2);\n\n% (c) P(75 \u2264 X \u2264 85)\nPc2 = normcdf(85, mu2, sigma2) - normcdf(75, mu2, sigma2);\n\n% (d) 5th percentile\nP5_2 = norminv(0.05, mu2, sigma2);\n\n% (e) 60th percentile\nP60_2 = norminv(0.60, mu2, sigma2);\n\n% (f) 97th percentile\nP97_2 = norminv(0.97, mu2, sigma2);\n\n% Display results for normal distribution N(75,8)\nfprintf('Normal Distribution N(75,8) Results:\\n');\nfprintf('P(X = 70): %f\\n', P70);\nfprintf('P(X = 73): %f\\n', P73);\nfprintf('P(75 \u2264 X \u2264 85): %f\\n', Pc2);\nfprintf('5th percentile: %f\\n', P5_2);\nfprintf('60th percentile: %f\\n', P60_2);\nfprintf('97th percentile: %f\\n', P97_2);<\/code><\/pre>\n\n\n\n
\n\n\n\n
Explanation (300 words)<\/h3>\n\n\n\n
This MATLAB script calculates probabilities and percentiles for both a standard normal distribution (mean = 0, standard deviation = 1) and a normal distribution with mean 75 and standard deviation 8.<\/p>\n\n\n\n
For Part 1<\/strong>, we analyze the standard normal distribution, using normpdf<\/code> for point probabilities and normcdf<\/code> for cumulative probabilities. However, for continuous distributions, the probability at a single point (e.g., P(X = -2) or P(X = 1)) is technically zero, though the probability density function (normpdf<\/code>) provides an estimate of density at that point. To find the probability of an interval, we subtract cumulative distribution function (CDF) values. Percentiles are computed using norminv<\/code>, which is the inverse CDF function.<\/p>\n\n\n\n
For Part 2<\/strong>, we repeat the process for a normal distribution with mean 75 and standard deviation 8. The calculations are analogous to Part 1, but with different mean and standard deviation values. Again, point probabilities are computed using normpdf<\/code>, while cumulative probabilities for intervals are determined using normcdf<\/code>. The 5th, 60th, and 97th percentiles are found using norminv<\/code>.<\/p>\n\n\n\n
These computations are useful in statistics and engineering, particularly in hypothesis testing, risk assessment, and quality control. The standard normal distribution serves as a benchmark for many statistical applications, while real-world distributions often involve different means and variances. MATLAB provides efficient built-in functions to handle these computations, making it a valuable tool for probability and statistical analysis.<\/p>\n","protected":false},"excerpt":{"rendered":"
part 1 Use MATLAB\u00ae to calculate the following probabilities and percentiles for the standard normal distribution:a. ??(??=-2)b. ??(??=1)c. ??(-0.4=??=1.6)d. The 5th percentilee. The 75th percentilef. The 99th percentile part 2 Use MATLAB\u00ae to calculate the following probabilities and percentiles for the ??(75,8) distribution:a. ??(??=70)b. ??(??=73)c. ??(75=??=85)d. The 5th percentilee. The 60th percentilef. The 97th percentile […]<\/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-191041","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191041","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=191041"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191041\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=191041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=191041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=191041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}