{"id":2894,"date":"2020-01-07T02:19:34","date_gmt":"2020-01-07T01:19:34","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=2894"},"modified":"2024-03-29T08:36:04","modified_gmt":"2024-03-29T07:36:04","slug":"how-to-calculate-and-solve-for-standard-normal-variable-probability","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2020\/01\/07\/how-to-calculate-and-solve-for-standard-normal-variable-probability\/","title":{"rendered":"How to Calculate and Solve for Standard Normal Variable | Probability"},"content":{"rendered":"

\"\"<\/p>\n

The image above represents standard normal variable. To calculate the probability of standard normal variable, three essential parameters are needed and these parameters are value (x), mean (\u03bc)\u00a0<\/strong>and\u00a0standard deviation (\u03c3).<\/strong><\/p>\n

The formula for calculating standard normal variable:<\/p>\n

z =\u00a0(x – \u03bc)<\/sup> \u2044 \u03c3<\/sub><\/p>\n

Where;<\/p>\n

z = Standard Normal Variable
\nx = Value
\n\u03bc = Mean
\n\u03c3 = Standard Deviation<\/p>\n

Let’s solve an example;
\nFind the standard normal variable when the value is 4, the mean is 20 and the standard deviation is 26.<\/p>\n

This implies that;<\/p>\n

x = Value = 4
\n\u03bc = Mean = 20
\n\u03c3 = Standard Deviation = 26<\/p>\n

z =\u00a0(x – \u03bc)<\/sup> \u2044 \u03c3<\/sub>
\nSo, z = (4 – 20)<\/sup> \u2044 26<\/sub>
\nz =\u00a0(-16)<\/sup> \u2044 26<\/sub>
\nz = -0.615<\/p>\n

Therefore, the standard normal variable<\/strong> is -0.615.<\/strong><\/p>\n

Calculating for Value when the Standard Normal Variable, the Mean and the Standard Deviation is Given<\/strong><\/h3>\n

x = z\u03c3 + \u03bc<\/p>\n

Where;<\/p>\n

x = Value
\nz = Standard Normal Variable
\n\u03bc = Mean
\n\u03c3 = Standard Deviation<\/p>\n

Let’s solve an example;
\nFind the value when the standard normal variable is 12, the mean is 10 and the standard deviation is 4.<\/p>\n

This implies that;<\/p>\n

z = Standard Normal Variable = 12
\n\u03bc = Mean = 10
\n\u03c3 = Standard Deviation = 4<\/p>\n

x = z\u03c3 + \u03bc
\nThen, x = (12)(4) + 10
\nx = 48 + 10
\nx = 58<\/p>\n

Therefore, the\u00a0value\u00a0<\/strong>is\u00a058.<\/strong><\/p>\n

Calculating for Mean when the Standard Normal Variable, the Value and the Standard Deviation are Given<\/strong><\/h3>\n

\u03bc = x – z\u03c3<\/p>\n

Where;<\/p>\n

\u03bc = Mean
\nz = Standard Normal Variable
\nx = Value
\n\u03c3 = Standard Deviation<\/p>\n

Let’s solve an example;
\nFind the mean when the standard normal variable is 6, the value is 30 and the standard deviation is 3.<\/p>\n

This implies that;<\/p>\n

z = Standard Normal Variable = 6
\nx = Value = 30
\n\u03c3 = Standard Deviation = 3<\/p>\n

\u03bc = x – z\u03c3
\nSo, \u03bc = 30 – (6)(3)
\n\u03bc = 30 – 18
\n\u03bc = 12<\/p>\n

Therefore, the\u00a0mean\u00a0<\/strong>is\u00a012.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Standard Deviation | Probability<\/a><\/p>\n

Calculating for Standard Deviation when the Standard Normal Variable, the Value and the Mean are Given<\/strong><\/h3>\n

\u03c3 = x – \u03bc<\/sup> \/ z<\/sub><\/p>\n

Where;<\/p>\n

\u03c3 = Standard Deviation
\nz = Standard Normal Variable
\nx = Value
\n\u03bc = Mean<\/p>\n

Let’s solve an example;
\nFind the standard deviation when the standard normal variable is 8, the value is 40 and the mean is 8.<\/p>\n

This implies that;<\/p>\n

z = Standard Normal Variable = 8
\nx = Value = 40
\n\u03bc = Mean = 8<\/p>\n

\u03c3 = x – \u03bc<\/sup> \/ z<\/sub>
\nSo, \u03c3 = 40 – 8<\/sup> \/ 8<\/sub>
\n\u03c3 = 32<\/sup> \/ 8<\/sub>
\n\u03c3 = 4<\/p>\n

Therefore, the\u00a0standard deviation\u00a0<\/strong>is\u00a04.<\/strong><\/p>\n

How to Calculate Standard Normal Variable Using Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the standard normal variable.<\/p>\n

To get the answer and workings of the standard normal variable using the Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n

You can get this app via any of these means:<\/p>\n

Web<\/strong>\u00a0\u2013\u00a0https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n

To get access to the\u00a0professional\u00a0<\/strong>version via web, you need to\u00a0register<\/strong>\u00a0and\u00a0subscribe\u00a0<\/strong>for\u00a0NGN 1,500\u00a0<\/strong>per\u00a0annum<\/strong>\u00a0to have utter access to all functionalities.
\nYou can also try the\u00a0demo\u00a0<\/strong>version via\u00a0https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n

Android (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a>
\nAndroid (Free)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a>
\nApple (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a>
\nOnce, you have obtained the calculator encyclopedia app, proceed to the\u00a0Calculator Map,\u00a0<\/strong>then click on\u00a0Probability<\/strong>\u00a0<\/strong>under\u00a0Mathematics<\/strong>.<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0Standard Normal Variable<\/strong>\u00a0<\/strong>under\u00a0Probability<\/strong><\/p>\n

\"\"<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the standard normal variable according to the respective parameters which are the\u00a0value (x), mean (\u03bc)\u00a0<\/strong>and\u00a0standard deviation (\u03c3).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the value (x)<\/strong> is 4<\/strong>, mean (\u03bc) <\/strong>is 20 <\/strong>and\u00a0standard deviation (\u03c3)\u00a0<\/strong>is\u00a026.<\/strong><\/p>\n

\"How<\/p>\n

Finally, Click on Calculate<\/p>\n

\"How<\/p>\n

As you can see from the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the standard normal variable and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents standard normal variable. To calculate the probability of standard normal variable, three essential parameters…","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":""},"categories":[4],"tags":[84,56,188,87,784,818,819,733],"class_list":["post-2894","post","type-post","status-publish","format-standard","category-mathematics","tag-calculator-encyclopedia","tag-mathematics","tag-mean","tag-nickzom-calculator","tag-probability","tag-standard-deviation","tag-standard-normal-variable","tag-value","cs-entry"],"yoast_head":"\nHow to Calculate and Solve for Standard Normal Variable | Probability<\/title>\n<meta name=\"description\" content=\"Master and learn How to Calculate and Solve for Standard Normal Variable in probability. 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