**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.

Answered: Image /qna-images/answer/dc44e887-4d86-4639-a006-41ff65f733a2.jpg

Answered: If z is a standard normal variable,…

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

See similar textbooks

Related questions

Q: Find the value of Z from the standard normal table such that the probability between Z and –Z is…

A: We use z distribution table to find the required solution.

Q: Assume you have a normal distribution. What is the probability of obtaining a z less than the…

A: Assume we have a normal distribution

Q: Z is the standard normal distribution. Find the indicated probability of P(0.61 ≤ Z ≤ 1.5)

A: Step 1:Evaluate the indicated probability:P(0.61≤Z≤1.5).Step 2:We know that…

Q: If z is a standard normal variable, find the probability when z is less than 1.98 0.9078 0.0239…

A: Z is a standard normal variableProbability that z is less than 1.98 is given by,

Q: Let Z have Standard Normal distribution. Find the probability that Z > 1.23. Write your answer in…

A: It is given that Z > 1.23.

Q: If Z is a standard normal variable find P(Z>-3.00)

A: It is an important part of statistics. It is widely used.

Q: Find the indicated probability using the standard normal distribution. P(-3.02 <z< 0)

A: Standard Normal Distribution: A random variable z is said to be a standard normal variable if z…

Q: ind P(Z < 2.04) where Z is the standard normal random variable. Round to 4 decimal places. Answer:

A: given data standard normal distribution Z~N(0,1) P(z<2.04) = ?

Q: Let z be a random variable with a standard normal distribution. Find the indicated probability.…

A: P( - 2.18 ≤ Z ≤ - 0.46 ) = P( Z ≤ - 0.46 ) – P(Z ≤ - 2.18) = 0.322758 – 0.014629 = 0.308129 ≈ 0.3081…

Q: tandard normal variable Z, find the probability P(Z>−0.34)P(Z>-0.34) : P(Z>−0.34)=P(Z>-0.34)=

A: given data,stanadard normal curve X~N(0,1)μ=0σ=1we have to find out the given probability

Q: Find the indicated probability using the standard normal distribution. P(0<z<0.395)

A: The given z-scores are z=0 and z=0.395.

Q: If z is a standard normal variable, find the probability that z is between − 2.07 a n d 3.28 (…

A: Draw the normal curve and shade the area between z=-2.07 and z=3.28.

Q: Find the indicated probability using the standard normal distribution. P(z<−1.49)

A: The required probability is calculated as follows: Pz<-1.49=0.0681

Q: Find the indicated probability using the standard normal distribution. P(z>-0.945)

A: The objective of this question is to find the probability that a value from a standard normal…

Q: Find the indicated probability using the standard normal distribution. P(z>1.31)

A: The objective of this question is to find the probability that a value from a standard normal…

Q: Find P(Z > 1.6) where Z is the standard normal random variable. Round to 4 decimal places. Answer:

A: given data standard normal distribution Z~N(0,1) P(Z≥1.6) = ?

Q: Find the indicated probability using the standard normal distribution. P(z< - 0.44)

A: We've to check the probability at -0.4 on vertical line and 0.04 on horizontal line in standard…

Q: Let z be a random variable with a standard normal distribution. Find the indicated probability.…

Q: Let z be a random variable with a standard normal distribution. Find the indicated probability…

A: we have to find P(z ≤ 1.5)....

Q: If z is a standard normal variable, find the probability: P(-0.73 < z < 2.27) Remember to use…

Q: Find the probability using the normal table (opens in new window). P(p ≥ 0.13) = P(z ≥ 1.5) = (Click…

A: The z-score is 1.5

Q: f z

A: As, z is a standard number variable, so Mean (μ) = 0 Standard Deviation (σ) = 1 So, Z = z-01~N(0,1)

Q: let z be the standard normal random variable. 2 Find P(z < 1.24) a 0.9371 b 0.8925 c…

A: Given that Z be the standard normal random variable Find P(z<1.24)=

Q: Let z be a random variable with a standard normal distribution. Find the indicated probability of…

A: The z-scores are -2.05 and 1.00.

Q: If z is a standard normal variable, find the probability. P(z < 0.85) Group of answer choices…

A: Given that:Z is standard normal Distributed with i.e. mean µ =0 and standard deviation σ =1 By…

Q: Find the indicated probability using the standard normal distribution. P(z2.68)

A: We have given P( <-2.68) Or Z>2.68)

Q: Assume that x has a normal distribution with the specified mean and standard deviation. Find the…

A: Mean = 4 Standard deviation = 6

Q: Let Z be a standard normal random variable. Calculate P(-1.064 < Z).

A: Given that Z follows standard normal distribution. Then we will use standard normal table to…

Q: A normal distribution has a mean of u = 90 with o = 15. Find the following %3D %3D probabilities: a.…

A: Note- As per our policy we can answer only the first 3 sub-parts of a question. If you want…

Q: assume that x has a normal distribution with the specified mean and standard deviation. Find the…

A: The standard normal distribution is the improvisation of normal distribution. If we substitute…

Q: Find the indicated probability using the standard normal distribution. P( -0.97< z<0)

A: The objective of this question is to find the probability that a value from a standard normal…

Q: If z is a standard normal variable, find the probability. P(-0.77<z<2.29) O0.8386 O 0.7904 O 0.7683…

A: GivenP(-0.77<z<2.29)

Q: Find the indicated probability using the standard normal distribution. P(- 2.45<z <0)

A: The objective of this question is to find the probability that a value from a standard normal…

Q: Find the indicated probability using the standard normal distribution. P(−0.34<z<0

A: Given, P(−0.34<z<0)

Q: Find P(-1.77 < Z ≤ 2.32) where Z is the standard normal random variable.

A: It is given that the Z be a standard normal random variable.

Q: Find the indicated probability using the standard normal distribution. P(z1.82)

A: P(z<-1.82 or z>1.82)=?

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

Find the indicated probability using the standard normal distribution. P(z < 1.64)
If z is a standard normal variable, find the probability. P<−0.77<z2.25 0.8415 0.7671 0.7916 0.8264
Find the value of Z from the standard normal table such that the probability between Z and –Z is 0.8664.
Find the indicated probability using the standard normal distribution. P(z< 0.68)
Find P(Z < -0.51) where Z is the standard normal random variable. Round to 4 decimal places. Answer:
Let Z be the standard normal random variable. Find P(Z>0.50) 0.0228 0.9772 0.5000 0.3085 0.6915
Assume you have a normal distribution. What is the probability of obtaining a z greater than the following?: +1.645 +2.322 -0.407 -7.091 +0.950
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(z z 1.44) =
If z is a standard normal variable, find the probability. P(Z < 0.97) O 0.1660 0.8340 O 0.8078 0.8315
let z be a random variable with a standard normal distribution. find the indicated probability P (-0.73< z< 3.12)