/*! 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 27 Find the \(z\) value for each of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 27

Find the \(z\) value for each of the following \(x\) values for a normal distribution with \(\mu=30\) and \(\sigma=5\) a. \(x=39\) b. \(x=19\) c. \(x=24\) d. \(x=44\)

Short Answer

Expert verified
The corresponding \( z \) values for the given \( x \) values are: \n a. \( z = 1.8 \) \n b. \( z = -2.2 \) \n c. \( z = -1.2 \) \n d. \( z = 2.8 \)

Step by step solution

01

Understand the Formula

In a normally distributed sample or population, \( z \) values can be calculated using the following formula: \( z = \frac{x - \mu}{\sigma} \), where \( \mu \) is the mean, \( \sigma \) is the standard deviation, and \( x \) is the value for which we need to find the \( z \) value.
02

Substitute the values of \( x \), \( \mu \), and \( \sigma \) into the formula

Now, for each \( x \), substitute the values of \( x \), \( \mu \), and \( \sigma \) into the formula. The four equations are as follows: \n a. \( z = \frac{39 - 30}{5} \) \n b. \( z = \frac{19 - 30}{5} \) \n c. \( z = \frac{24 - 30}{5} \) \n d. \( z = \frac{44 - 30}{5} \)
03

Solve the equations

Soling the equations from step 2 would give us: \n a. \( z = 1.8 \) \n b. \( z = -2.2 \) \n c. \( z = -1.2 \) \n d. \( z = 2.8 \)

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

The Bank of Connecticut issues Visa and MasterCard credit cards. It is estimated that the balances on all Visa credit cards issued by the Bank of Connecticut have a mean of \(\$ 845\) and a standard deviation of \(\$ 270\). Assume that the balances on all these Visa cards follow a normal distribution. a. What is the probability that a randomly selected Visa card issued by this bank has a balance between \(\$ 1000\) and \(\$ 1440 ?\) h. What percentage of the Visa cards issued by this bank have a balance of \(\$ 730\) or more?

For the standard normal distribution, what is the area within three standard deviations of the mean?

One of the cars sold by Walt's car dealership is a very popular subcompact car called Rhino. The final sale price of the basic model of this car varies from customer to customer depending on the negotiating skills and persistence of the customer. Assume that these sale prices of this car are normally distributed with a mean of \(\$ 19,800\) and a standard deviation of \(\$ 350\). a. Dolores paid \(\$ 19,445\) for her Rhino. What percentage of Walt's customers paid less than Dolores for a Rhino? b. Cuthbert paid \(\$ 20,300\) for a Rhino. What percentage of Walt's customers paid more than Cuthbert for a Rhino?

Find the following probabilities for the standard normal distribution. a. \(P(z<-2.34)\) b. \(P(.67 \leq z \leq 2.59)\) c. \(P(-2.07 \leq z \leq-.93)\) d. \(P(z<1.78)\)

A psychologist has devised a stress test for dental patients sitting in the waiting rooms. According to this test, the stress scores (on a scale of 1 to 10 ) for patients waiting for root canal treatments are found to be approximately normally distributed with a mean of \(7.59\) and a standard deviation of \(.73\). a. What percentage of such patients have a stress score lower than \(6.0\) ? b. What is the probability that a randomly selected root canal patient sitting in the waiting room has a stress score between \(7.0\) and \(8.0\) ? c. The psychologist suggests that any patient with a stress score of \(9.0\) or higher should be given a sedative prior to treatment. What percentage of patients waiting for root canal treatments would need a sedative if this suggestion is accepted?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Decision Maths

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.