/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 Determine the value of \(z^{*}\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 22

Determine the value of \(z^{*}\) such that a. \(z^{*}\) and \(-z^{*}\) separate the middle \(95 \%\) of all \(z\) values from the most extreme \(5 \%\) b. \(z^{*}\) and \(-z^{*}\) separate the middle \(90 \%\) of all \(z\) values from the most extreme \(10 \%\) c. \(z^{*}\) and \(-z^{*}\) separate the middle \(98 \%\) of all \(z\) values from the most extreme \(2 \%\) d. \(z^{*}\) and \(-z^{*}\) separate the middle \(92 \%\) of all \(z\) values from the most extreme \(8 \%\)

Short Answer

Expert verified
The z-values for (a) 95% middle is 卤1.96, (b) 90% middle is 卤1.645, (c) 98% middle is 卤2.33, and (d) 92% middle is 卤1.75.

Step by step solution

01

Understanding the concept

A z-table, also called the standard normal table, is a mathematical table that allows us to know the percentage of values below (to the left of) a z-score in a standard normal distribution. For this problem, each case is a two-tail problem where you have some percentage in the middle and the rest is equally distributed in both tails. In each case, you need to first identify the total tail percentage and divide by two as the Z-table works for the area to the left of the z-score.
02

Locate z-score for part (a)

For part (a), the middle 95% means you have 5% in the tails. Since this is a two-tailed test, you have 2.5% in each tail. In this case, look for closest to 0.9750 (0.5000 + 0.4750) in the Z-table which gives a z-score of 1.96.
03

Locate z-score for part (b)

For part (b), the middle 90% means you have 10% in the tails. Therefore 5% in each tail. Look for closest to 0.9500 (0.5000 + 0.4500) in the Z-table which gives a z-score of 1.645.
04

Locate z-score for part (c)

For part (c), the middle 98% means you have 2% in the tails. Therefore 1% in each tail. Look for closest to 0.9900 (0.5000 + 0.4900) in the Z-table which gives a z-score of 2.33.
05

Locate z-score for part (d)

For part (d), the middle 92% means you have 8% in the tails. Therefore, 4% in each tail. Look for closest to 0.9600 (0.5000 + 0.4600) in the Z-table which gives a z-score of 1.75.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Consider babies bom in the "normal" range of 37-43 weeks gestational age. Extensive data support the assumption that for such babies born in the United States, birth weight is normally distributed with mean \(3432 \mathrm{~g}\) and standard deviation \(482 \mathrm{~g}\) ("Are Babies Normal," The \(-302\) ). (The investigad data from a particular s intervals, the hisbut after further investi1 that this was due ht in grams and others measuring to the nearest ounce and then converting to grams. A modified choice of class intervals that allowed for this measurement difference gave a histogram that was well described by a normal distribution.) a. What is the probability that the birth weight of a randomly selected baby of this type exceeds \(4000 \mathrm{~g}\) ? is between 3000 and \(4000 \mathrm{~g}\) ? b. What is the probability that the birth weight of a randomly selected baby of this type is either less than \(2000 \mathrm{~g}\) or greater than \(5000 \mathrm{~g}\) ? c. What is the probability that the birth weight of a randomly selected baby of this type exceeds \(7 \mathrm{lb}\) ? (Hint: \(1 \mathrm{lb}=453.59 \mathrm{~g} .\) ) d. How would you characterize the most extreme \(0.1 \%\) of all birth weights?

Let \(z\) denote a variable that has a standard normal distribution. Determine the value \(z^{*}\) to satisfy the following conditions: a. \(P\left(zz^{*}\right)=.02\) e. \(P\left(z>z^{*}\right)=.01\) f. \(P\left(z>z^{*}\right.\) or \(\left.z<-z^{*}\right)=.20\)

Because \(P(z<0.44)=.67,67 \%\) of all \(z\) values are less than \(0.44\), and \(0.44\) is the 67 th percentile of the standard normal distribution. Determine the value of each of the following percentiles for the standard normal distribution (Hint: If the cumulative area that you must look for does not appear in the \(z\) table, use the closest entry): a. The 91st percentile (Hint: Look for area \(.9100 .\) ) b. The 77 th percentile c. The 50 th percentile d. The 9 th percentile e. What is the relationship between the 70 th \(z\) percentile and the \(30 \mathrm{th} z\) percentile?

Consider the following sample of 25 observations on the diameter \(x\) (in centimeters) of a disk used in a certain system. \(\begin{array}{lllllll}16.01 & 16.08 & 16.13 & 15.94 & 16.05 & 16.27 & 15.89 \\ 15.84 & 15.95 & 16.10 & 15.92 & 16.04 & 15.82 & 16.15 \\ 16.06 & 15.66 & 15.78 & 15.99 & 16.29 & 16.15 & 16.19 \\ 16.22 & 16.07 & 16.13 & 16.11 & & & \end{array}\) The 13 largest normal scores for a sample of size 25 are \(1.965,1.524,1.263,1.067,0.905,0.764,0.637,0.519\) \(0.409,0.303,0.200,0.100\), and \(0 .\) The 12 smallest scores result from placing a negative sign in front of each of the given nonzero scores. Construct a normal probability plot. Does it appear plausible that disk diameter is normally distributed? Explain.

Classify each of the following numerical variables as either discrete or continuous: a. The fuel efficiency (in miles per gallon) of an automobile b. The amount of rainfall at a particular location during the next year c. The distance that a person throws a baseball d. The number of questions asked during a 1 -hr lecture e. The tension (in pounds per square inch) at which a tennis racket is strung f. The amount of water used by a household during a given month g. The number of traffic citations issued by the highway patrol in a particular county on a given day
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

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.