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Could you help explain how you find z = -2.326 from the z table, please? Thank you. Much appreciated!

Could you help explain how you find z = -2.326 from the z table, please? Thank you. Much appreciated!

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Could you help explain how you find z = -2.326 from the z table, please? Thank you. Much appreciated!

**Statistical Analysis of Assembly Time for Medical Devices** A statistical analysis of a very large sample of fully-assembled medical devices indicates that the length of the assembly time required is normally distributed with a mean value of 240 seconds and a standard deviation of 40 seconds. Question: 1% of all assemblies will require less than how many seconds? Round the nearest second (integer answer). Note: There are no graphs or diagrams associated with this text.
Transcribed Image Text:**Statistical Analysis of Assembly Time for Medical Devices** A statistical analysis of a very large sample of fully-assembled medical devices indicates that the length of the assembly time required is normally distributed with a mean value of 240 seconds and a standard deviation of 40 seconds. Question: 1% of all assemblies will require less than how many seconds? Round the nearest second (integer answer). Note: There are no graphs or diagrams associated with this text.
Sure, here is the transcription of the image: --- **Step 2** \[ P(z < z_c) = 0.01 \] ∴ \( z = -2.326 \) (∵ z-table) \[ z = \frac{X - μ}{σ} \] \[ -2.326 = \frac{X - 240}{40} \] ∴ \( X = 146.96 \) \[ x ≈ \boxed{147} \, \text{seconds} \] --- ### Explanation: In this step, we are working with the z-score formula to find \( X \), given a probability and a specified mean (\( μ \)) and standard deviation (\( σ \)). - We start with the cumulative probability \( P(z < z_c) = 0.01 \). - From the z-table, we find the corresponding z-score to be \( z = -2.326 \). - Using the z-score formula: \[ z = \frac{X - μ}{σ} \] - Given: \( μ = 240 \) and \( σ = 40 \) - We substitute the values into the formula: \[ -2.326 = \frac{X - 240}{40} \] - Solving for \( X \), we get \( X = 146.96 \) which is approximately \( 147 \) seconds.
Transcribed Image Text:Sure, here is the transcription of the image: --- **Step 2** \[ P(z < z_c) = 0.01 \] ∴ \( z = -2.326 \) (∵ z-table) \[ z = \frac{X - μ}{σ} \] \[ -2.326 = \frac{X - 240}{40} \] ∴ \( X = 146.96 \) \[ x ≈ \boxed{147} \, \text{seconds} \] --- ### Explanation: In this step, we are working with the z-score formula to find \( X \), given a probability and a specified mean (\( μ \)) and standard deviation (\( σ \)). - We start with the cumulative probability \( P(z < z_c) = 0.01 \). - From the z-table, we find the corresponding z-score to be \( z = -2.326 \). - Using the z-score formula: \[ z = \frac{X - μ}{σ} \] - Given: \( μ = 240 \) and \( σ = 40 \) - We substitute the values into the formula: \[ -2.326 = \frac{X - 240}{40} \] - Solving for \( X \), we get \( X = 146.96 \) which is approximately \( 147 \) seconds.
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