Problem 34 A normal distribution has standa... [FREE SOLUTION] (2024)

Table of Contents
Short Answer Step by step solution Calculate the median (\(\mu\)) Find the 16th percentile \(P_{16}\) One App. One Place for Learning. Most popular questions from this chapter Recommended explanations on Math Textbooks Probability and Statistics Statistics Pure Maths Mechanics Maths Theoretical and Mathematical Physics Logic and Functions Study anywhere. Anytime. Across all devices.

Get started for free

Log In Start studying!

Get started for free Log out

Chapter 17: Problem 34

A normal distribution has standard deviation \(\sigma=12.3\) points and the 84th percentile of the distribution is \(P_{84}=66.7\) points. (a) Find the median \(\mu\). (b) Find the 16 th percentile \(P_{16}\).

Short Answer

Expert verified

The median (\(\mu\)) is 54.4 and the 16th percentile \(P_{16}\) is 42.1.

Step by step solution

01

Calculate the median (\(\mu\))

Since the value of the 84th percentile is one standard deviation above the mean, we subtract one standard deviation from the P84 value to obtain the mean (\(\mu\)). Hence, \(\mu = P_{84} - \sigma = 66.7 - 12.3 = 54.4)\).

02

Find the 16th percentile \(P_{16}\)

The 16th percentile falls one standard deviation below the mean in a standard normal distribution. Therefore, subtract the standard deviation from the mean. So, \(P_{16} = \mu - \sigma = 54.4 - 12.3 = 42.1\).

See Also
. The average monthly rainfall (AMR) in inches is a random variable with the cumulative distribution...POS1500-HPR GOOD HEALTH STATUS AND NORMAL WEIGHT PREVENT CHRONIC PAINGeneral Instructions > Assignment should not be copied, should be clear, readable and well presented. > Maximum number of group member must be Six. > Submission date: 22 / 10 / 2016 E.C 1. In a ceratin population an averge of 13 new cases of esophageal ca

One App. One Place for Learning.

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

Get started for free

Problem 34 A normal distribution has standa... [FREE SOLUTION] (3)

Most popular questions from this chapter

An honest die is rolled. If the roll comes out even \((2,4,\) or 6 ), you willwin \(\$ 1 ;\) if the roll comes out odd \((1,3,\) or 5\()\), you will lose \(\$ 1 .\)Suppose that in one evening you play this game \(n=2500\) times in a row. (a) Estimate the probability that by the end of the evening you will not havelost any money. (b) Estimate the probability that the number of "even rolls" (roll a 2, 4, or6) will fall between 1250 and 1300 . (c) Estimate the probability that you will win \(\$ 100\) or more.In a normal distribution with mean \(\mu=50 \mathrm{lb},\) a weight of \(x=84\)lb. has a z-value of 2 . Find the standard deviation \(\sigma\).The distribution of weights for one-month-old baby girls is approximatelynormal with mean \(\mu=4.5 \mathrm{~kg}\) and standard deviation \(\sigma=0.4\mathrm{~kg}\) (a) Suppose that a one-month-old girl weighs \(5.3 \mathrm{~kg}\). Approximatelywhat weight percentile is she in? (b) Suppose that a one-month-old girl weighs \(5.7 \mathrm{~kg}\). Approximatelywhat weight percentile is she in? (c) Suppose that a one-month-old girl is in the 25 th percentile in weight.Estimate her weight.The distribution of weights for 12 -month-old baby boys has mean \(\mu=10.5\mathrm{~kg}\) and standard deviation \(\sigma=1.2 \mathrm{~kg} .\) (a) Suppose that a 12 -month-old boy weighs \(11.3 \mathrm{~kg}\). Approximatelywhat weight percentile is he in? (b) Suppose that a 12 -month-old boy weighs \(8.1 \mathrm{~kg}\). Approximatelywhat weight percentile is he in? (c) Suppose that a 12 -month-old boy is in the 84 th percentile in weight.Estimate his weight.In a normal distribution, the data value \(x_{1}=20\) has a \(z\) -value\(\left(z_{1}\right)\) of -2 and the data value \(x_{2}=100\) has a \(z\) -value\(\left(z_{2}\right)\) of 3 . Find the mean \(\mu\) and the standard deviation\(\sigma .\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

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

This website uses cookies to improve your experience. We'll assume you're ok with this, but you can opt-out if you wish. Accept

Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.

Necessary

Always Enabled

Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.

Non-necessary

Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.

Problem 34 A normal distribution has standa... [FREE SOLUTION] (2024)
Top Articles
19 Drool-Worthy Vegan Pizza Recipes
Best Restaurants in Varachha Sheri, Rughanathpura, Surat | May 2024
Mount Pleasant, SC Hiking Trails & Trail Maps
What the 'King of Deflections' Delon Wright brings to the Bucks defense
Roto Lineup Optimizer
Prc Lackland Afb
Smitedataming
Peer-Reviewed Clinical Journals | Impact Factors Rankings
Philadelphia PA Real Estate - Philadelphia PA Homes For Sale | Zillow
Codes et commandes Bedwars (juillet 2024) - Play Trucos
Craigslist Org East Texas
What Every Frenchwoman Wants دانلود زیرنویس
Latest Posts
Lemony Chickpea Feta Salad | Nyssa's Kitchen
Try delicious ratatouille for dinner tonight!
Article information

Author: Laurine Ryan

Last Updated:

Views: 5914

Rating: 4.7 / 5 (77 voted)

Reviews: 92% of readers found this page helpful

Author information

Name: Laurine Ryan

Birthday: 1994-12-23

Address: Suite 751 871 Lissette Throughway, West Kittie, NH 41603

Phone: +2366831109631

Job: Sales Producer

Hobby: Creative writing, Motor sports, Do it yourself, Skateboarding, Coffee roasting, Calligraphy, Stand-up comedy

Introduction: My name is Laurine Ryan, I am a adorable, fair, graceful, spotless, gorgeous, homely, cooperative person who loves writing and wants to share my knowledge and understanding with you.