Standard Normal Distribution — Hypothesis Testing

The normal distribution X∼N(0,1), μ = 0 and σ = 1, is called the standard normal distribution, and its distribution function is:


A value from any normal distribution can be transformed into its corresponding value on a standard normal distribution using the following formula:

$$Z =\frac{X - μ}{σ}$$

where Z is the value on the standard normal distribution, X is the value on the original distribution, μ is the mean of the original distribution, and σ is the standard deviation of the original distribution.

$$E(Z)= E\biggl(\frac{X - μ}{σ}\biggr)=\frac{E(X) - μ}{σ}=0$$ $$Var(Z)=Var\biggl(\frac{X - μ}{σ}\biggr)=\frac{Var(X)}{σ^2}=1$$

To computing probabilities for normal distributions, convert to standard value and lookup the distribution function tables for the standard normal distribution:

$$P(X≤b)→P\biggl(Z≤\frac{b - μ}{σ}\biggr)$$

Note: The probabilities may also be obtained using the NORM.DIST function in Excel. The Excel NORM.INV function returns the variable value, given the parameters and the probability.

Previous     Next

Use the Search Bar to find content on MarketingMind.

Marketing Analytics Workshop

Marketing Analytics Workshop

In an analytics-driven business environment, this analytics-centred consumer marketing workshop is tailored to the needs of consumer analysts, marketing researchers, brand managers, category managers and seasoned marketing and retailing professionals.

What they SHOULD TEACH at Business Schools

What they SHOULD TEACH at Business Schools

Is marketing education fluffy too?

Experiential Learning via Simulators | Best Way to Train Marketers

Experiential Learning via Simulators | Best Way to Train Marketers

Marketing simulators impart much needed combat experiences, equipping practitioners with the skills to succeed in the consumer market battleground. They combine theory with practice, linking the classroom with the consumer marketplace.