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Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z > c) = 0.0143, find c. C =

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z > c) = 0.0143, find c. C =

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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### Understanding Z-Scores and their Distribution Z-scores represent standard deviations away from the mean. They follow a normal distribution with the following parameters: - Mean (μ) = 0 - Standard Deviation (σ) = 1 When dealing with Z-scores, you can determine the probability of observing a value greater than a certain threshold. --- #### Example Problem: Assume that Z-scores are normally distributed with a mean of 0 and a standard deviation of 1. Given: \[ P(z > c) = 0.0143 \] Find the value of \( c \): \[ c = \] Here, you need to find the value of \( c \) such that the probability of a Z-score being greater than \( c \) is 0.0143. ##### Solution Approach: 1. Use the standard normal distribution table or a calculator that provides the inverse of the cumulative distribution function (CDF) for the normal distribution. 2. Locate the probability value close to 0.0143 in the standard normal distribution table. 3. The corresponding Z-score at this probability gives you the value of \( c \). This exercise aids in understanding how to work with the probabilities associated with Z-scores in a normal distribution context.
Transcribed Image Text:### Understanding Z-Scores and their Distribution Z-scores represent standard deviations away from the mean. They follow a normal distribution with the following parameters: - Mean (μ) = 0 - Standard Deviation (σ) = 1 When dealing with Z-scores, you can determine the probability of observing a value greater than a certain threshold. --- #### Example Problem: Assume that Z-scores are normally distributed with a mean of 0 and a standard deviation of 1. Given: \[ P(z > c) = 0.0143 \] Find the value of \( c \): \[ c = \] Here, you need to find the value of \( c \) such that the probability of a Z-score being greater than \( c \) is 0.0143. ##### Solution Approach: 1. Use the standard normal distribution table or a calculator that provides the inverse of the cumulative distribution function (CDF) for the normal distribution. 2. Locate the probability value close to 0.0143 in the standard normal distribution table. 3. The corresponding Z-score at this probability gives you the value of \( c \). This exercise aids in understanding how to work with the probabilities associated with Z-scores in a normal distribution context.
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