For a population with u= 40 and a =8, what is the z-score corresponding to X-34?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
100%
For a population with μ = 40 and σ = 8, what is the z-score corresponding to X = 34?

### Explanation

To find the z-score, use the formula:

\[ z = \frac{X - \mu}{\sigma} \]

Where:
- \( \mu \) is the mean of the population (40 in this case),
- \( \sigma \) is the standard deviation of the population (8 in this case),
- \( X \) is the value for which we are finding the z-score (34 in this case).

### Calculation

Applying the values:

\[ z = \frac{34 - 40}{8} \]

\[ z = \frac{-6}{8} \]

\[ z = -0.75 \]

The z-score is -0.75, indicating that the value 34 is 0.75 standard deviations below the mean.
Transcribed Image Text:For a population with μ = 40 and σ = 8, what is the z-score corresponding to X = 34? ### Explanation To find the z-score, use the formula: \[ z = \frac{X - \mu}{\sigma} \] Where: - \( \mu \) is the mean of the population (40 in this case), - \( \sigma \) is the standard deviation of the population (8 in this case), - \( X \) is the value for which we are finding the z-score (34 in this case). ### Calculation Applying the values: \[ z = \frac{34 - 40}{8} \] \[ z = \frac{-6}{8} \] \[ z = -0.75 \] The z-score is -0.75, indicating that the value 34 is 0.75 standard deviations below the mean.
Expert Solution
Step 1

Z-score is -0.75

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,