**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: Given that is a standard normal random variable, find for each situation (to 2 decimals). The area…

A: Given that Z is a standard normal random variable, We have to find the value of Z Where the areas…

Q: For the standard normal variable Z, find the probability P(Z>2.86)P(Z>2.86) : P(Z>2.86)=

A: Given data for the standard normal variable Z find the probability p(z>2.86)=?

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: 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 probab P(-0.25 <…

A: P(-0.25≤z≤0.55)=?

Q: Let z be a standard normal variable. Calculate each of the following probabilities: P(-2.58 ≤ z…

A: To calculate this probability, we can use the properties of the standard normal distribution. The…

Q: Find the probability, P(Z > -0.77) for a standard normal variable Z. 20 Find the probability,…

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: John plays a roulette 5 times; each time betting on red. The probability of red is 18/38=9/19. Let X…

A: For a random variable X~B(n,p), the pmf is P(X=x)=nCxpxqn-x ; x=0,1,2...n, p=probability…

Q: Find the indicated probability using the standard normal distribution P(z ˂ - 2.92 0r z ˃ 2.92) =

A: We have given the statement about standard normal distribution.

Q: If z is a standard normal variable, find the probability. P(z>0.72) O 0.3015 0.2358 O 0.2061 O…

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: let z be a random variable with a normal distribution/ Find the indicated probability P(z<-0.13) a…

Q: Find the following probability for the standard normal random variable z. e. P(z>0) f.…

A: Since the question has multiple subparts, as per the Bartleby policy, I will only solve first three…

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: x is a normally distributed random variable with mean 23 and standard deviation 7. What is the…

A: Mean(μ)=23 standard deviation(σ)=7

Q: For the standard normal random variable z, find P(z ≤ 0.57). Select one: A. 0.2877 B. 0.7157 C.…

A: Draw the normal curve and shade the area to the left of z=0.57.

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: 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: Estimate the indicated probability by using the normal distribution as an approximation to the…

A: Continuity Correction: The binomial and Poisson distributions are discrete random variables, whereas…

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: Given that z is a standard normal random variable, find z for each situation (to 2 decimals). The…

A: In this case, we need to find the z score values for the given areas.

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: Let z be a random variable with a standard normal distribution. Find P(–1.12 ≤ z ≤ 2.58). Use 4…

A: Given, let z be a random variable with standard normal distribution Find P(-1.12≤z≤2.58)

Q: Find P(Z < -1.26) where Z is the standard normal random variable. Round to 4 decimal places. Answer:

A: P(Z<-1.26)=?Z is the standard normal distribution.

Q: Find the probability using the normal distribution: P(−2.29<z<0)

A: standard normal distribution Z~N(0,1) μ= 0σ = 1 P(-2.29<Z<0) = ?

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: find the following probability. P(25<x<32)

A: Given that X follows N(mean = 25, SD = 4), then Z = (X - mean)/SD follows N(0,1)

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

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

Q: According to studies conducted by people who have too much time on their hands, one out of every…

A: The question is about sampling dist. Given : 1 out of every 8 letters written tends to E That means,…

Q: Let Z be a standard normal random variable. Use the z‐table to find P(Z > ‐1.30)?

A: Let Z be the random variable from standard normal distribution then, We will find P(Z > ‐1.30) =…

Q: The random variable X is related to e2. Find P(X>0.4).

A: It is given that the, The random variable X is related to e2 i.e. X ~ exp(2). We have to find P(X…

Q: Assume you have a normal distribution representing the likelihood of project completion times. The…

A: Let "X" be the likelihood of project completion times in days.

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

For the standard normal variable Z, find the probability P(Z < − 3.71): P(Z < - 3.71) = Submit Question (Round the answer to 4 decimal places)
Find P(Z > 0.88) where Z is the standard normal random variable. Round to 4 decimal places. Answer:
Find P(Z < -0.51) where Z is the standard normal random variable. Round to 4 decimal places. Answer:
Let x be a random variable that has a normal distribution with a mean of 40 and a standard deviation of 5. After converting the following x-values to z-values, find the following probabilities: P(x < 49) P(x > 55)
For the standard normal variable Z, find the probability P(Z>1.07)P(Z>1.07) : P(Z>1.07)=P(Z>1.07)= (Round the answer to 4 decimal places)
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
I have to find the value of the standard normal random variable. P (Z <= Zo) = .7054
let z be a random variable with a standard normal distribution. find the indicated probability P (-0.73< z< 3.12)
Find the probabilities for each using the standard normal distribution. P(z> 0.56)