# Let Z be the standard normal random variable. What is P (0 less than Z less than 2.50)?

## Question:

Let Z be the standard normal random variable. What is {eq}P (0 < Z < 2.50) {/eq}?

## Standard normal distribution

The standard normal distribution is the continuous probability distribution, the probability is either calculated from the standard normal distribution table and computer software, for example, Excel, R and SAS.

## Answer and Explanation:

The probability is calculated from the standard normal distribution table.

{eq}\begin{align*} P\left( {0 < Z < 2.5} \right) =& P\left( {Z < 2.5} \right) - P\left( {Z < 0} \right)\\ =& 0.99379 - 0.5\\ =& 0.4938 \end{align*} {/eq}

Therefore, the required probability is 0.4938.

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Normal Distribution of Data: Examples, Definition & Characteristics

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Chapter 13 / Lesson 7
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