Answered: 6. Let x be a random variable that…

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

Concept explainers

Topic Video

Question

$**Statistics and Probability Concepts in Medical Testing** ### Problem 6 Let $ x $ be a random variable that represents the white blood cell count per cubic milliliter of whole blood. Assume that $ x $ has a distribution that is approximately normal with a mean ($ \mu $) of 7500 and a standard deviation ($ \sigma $) of 1750. A test result of $ x \leq 3500 $ is an indication of leucopenia. This indicates bone marrow depression that may result in a viral infection. **a. Single Test Analysis** - **Question:** What is the probability that on a single test $ x $ is less than 3500? **b. Multiple Test Analysis** - **Question:** A patient is given 3 tests at regular intervals. What is the probability that the average of the three tests is less than 3500? ### Problem 7 The general ethnic profile of Denver is about 42% minority and 58% Caucasian. Suppose the city of Denver recently hired 56 new grounds and maintenance workers. It was claimed that the hiring practice is completely impartial without regard to ethnic... --- *Note: For Problem 6(a) and 6(b), it is important to make use of the Z-score formula and concepts of the normal distribution to determine the required probabilities. For Problem 7, concepts of proportion testing can be applied to validate the impartiality of hiring practices.* --- **Understanding the Z-Score Formula:** \[ Z = \frac{(X - \mu)}{\sigma} \] Where: - $ X $ is the value of the element - $ \mu $ is the mean of the population - $ \sigma $ is the standard deviation of the population For part (b), use the standard error of the mean (SEM): \[ SEM = \frac{\sigma}{\sqrt{n}} \] Where $ n $ is the number of tests (in this case, 3). Good luck with your computations, and remember, understanding the foundational concepts of statistics can drastically improve your ability to analyze real-world data.$

Transcribed Image Text:**Statistics and Probability Concepts in Medical Testing** ### Problem 6 Let $ x $ be a random variable that represents the white blood cell count per cubic milliliter of whole blood. Assume that $ x $ has a distribution that is approximately normal with a mean ($ \mu $) of 7500 and a standard deviation ($ \sigma $) of 1750. A test result of $ x \leq 3500 $ is an indication of leucopenia. This indicates bone marrow depression that may result in a viral infection. **a. Single Test Analysis** - **Question:** What is the probability that on a single test $ x $ is less than 3500? **b. Multiple Test Analysis** - **Question:** A patient is given 3 tests at regular intervals. What is the probability that the average of the three tests is less than 3500? ### Problem 7 The general ethnic profile of Denver is about 42% minority and 58% Caucasian. Suppose the city of Denver recently hired 56 new grounds and maintenance workers. It was claimed that the hiring practice is completely impartial without regard to ethnic... --- *Note: For Problem 6(a) and 6(b), it is important to make use of the Z-score formula and concepts of the normal distribution to determine the required probabilities. For Problem 7, concepts of proportion testing can be applied to validate the impartiality of hiring practices.* --- **Understanding the Z-Score Formula:** \[ Z = \frac{(X - \mu)}{\sigma} \] Where: - $ X $ is the value of the element - $ \mu $ is the mean of the population - $ \sigma $ is the standard deviation of the population For part (b), use the standard error of the mean (SEM): \[ SEM = \frac{\sigma}{\sqrt{n}} \] Where $ n $ is the number of tests (in this case, 3). Good luck with your computations, and remember, understanding the foundational concepts of statistics can drastically improve your ability to analyze real-world data.

Expert Solution

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Algebra$

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