**Finding the Probability for a Standard Normal Variable**In probability theory and statistics, the standard normal distribution is a very common continuous probability distribution. It is especially useful when dealing with statistical problems involving normal distributions.### Problem Statement:The problem presented is:"If $ z $ is a standard normal variable, find the probability: \[ P(z > 0.68) \]"### Options:The possible answers provided are:1. 0.24832. 0.20333. 0.31564. 0.2177### Explanation:To solve this problem, it's necessary to use the properties of the standard normal distribution.1. The standard normal distribution table (Z-table) provides the probability that a standard normal variable $ z $ will be less than a given value $ z $. This is represented as $ P(Z < z) $.2. To find $ P(z > 0.68) $: - First, find $ P(z < 0.68) $ using the Z-table. - Then use the fact that the total probability under the normal curve is 1, so $ P(z > 0.68) = 1 - P(z < 0.68) $.By checking the standard normal distribution table:- $ P(z < 0.68) $ is approximately 0.7517.Thus,\[ P(z > 0.68) = 1 - 0.7517 = 0.2483 \]### Conclusion:The correct answer is the first option, **0.2483**.### Answer Selection:- The selected answer is marked (0.2483) with a circling icon indicating it has been chosen. There is also a "check" (represented by an "X") and a "reset" (represented by a looped arrow) button indicating the option selected can be submitted or cleared.---This explanation outlines the steps needed to determine the probability of a standard normal variable being greater than a specified value. Understanding how to use the Z-table and properties of the standard normal distribution is essential for solving such problems.

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Math

Statistics

If z is a standard normal variable, find the probability. P(z>0.68)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

**Finding the Probability for a Standard Normal Variable**

In probability theory and statistics, the standard normal distribution is a very common continuous probability distribution. It is especially useful when dealing with statistical problems involving normal distributions.

### Problem Statement:
The problem presented is:

"If $ z $ is a standard normal variable, find the probability:
\[ P(z > 0.68) \]"

### Options:
The possible answers provided are:
1. 0.2483
2. 0.2033
3. 0.3156
4. 0.2177

### Explanation:
To solve this problem, it's necessary to use the properties of the standard normal distribution.

1. The standard normal distribution table (Z-table) provides the probability that a standard normal variable $ z $ will be less than a given value $ z $. This is represented as $ P(Z < z) $.

2. To find $ P(z > 0.68) $:
- First, find $ P(z < 0.68) $ using the Z-table.
- Then use the fact that the total probability under the normal curve is 1, so $ P(z > 0.68) = 1 - P(z < 0.68) $.

By checking the standard normal distribution table:
- $ P(z < 0.68) $ is approximately 0.7517.

Thus,
\[ P(z > 0.68) = 1 - 0.7517 = 0.2483 \]

### Conclusion:
The correct answer is the first option, **0.2483**.

### Answer Selection:
- The selected answer is marked (0.2483) with a circling icon indicating it has been chosen. There is also a "check" (represented by an "X") and a "reset" (represented by a looped arrow) button indicating the option selected can be submitted or cleared.

---

This explanation outlines the steps needed to determine the probability of a standard normal variable being greater than a specified value. Understanding how to use the Z-table and properties of the standard normal distribution is essential for solving such problems.

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