Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q. 10 (page 286)

Identify the distribution of the standardized version of a normally distributed variable.

Short Answer

Expert verified

The standard normal distribution is called z score or standard scorez=x-μσ.

Step by step solution

01

Given Information 

Identify the distribution of the standardized version of a normally distributed variable.

02

Explanation 

Take the normal distribution as an example.

A specific case of the normal distribution is the standardized normal distribution.

The standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one.

Hence, the standard normal distribution is called zscore or standard score. z=x-μσ.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

State the empirical rule as specialized to variables.

27. Lower Limb Surgery. The study "Intrathecal Sufentanil versus Fentanyl for Lower Limb Surgeries - A Randomized Controlled Trial" (Journal of Anesthesiology Clinical Pharmacology, Vol. 27 . Issue 1. pp. 67-73) by P. Motiani et al. compares two different agents, intrathecal Sufentanil and fentanyl, used in enhancing the anesthesiology of patients receiving major lower limb surgery. One variable compared between the two agents was the amount of blood loss during the surgery. Based on the study, we will assume that using fentanyl, the amount of blood loss during major lower limb surgery is normally distributed with mean 283.3mland standard deviation 83.3ml. Find the percentage of patients whose amount of blood loss during major lower limb surgery using fentanyl is

a. Less than 304ml.

b. Between 221and429ml

c. More than450ml.

Find the following z-scores.

a. Z0.03

b.z0.005

Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a special type of reverse-J-shaped distribution called an exponential distribution. The records also show that the mean time between arriving patients is 8.78 minutes.

a. Use the technology of your choice to simulate four random samples of75 interarrival times each.

b. Obtain a normal probability plot of each sample in part (a).

c. Are the normal probability plots in part (b) what you expected? Explain your answer.

Explain the relationship between percentages for a normally distributed variable and areas under the corresponding normal curve.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free