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15. Assume the random variable X is normally distributed with a mean of 22 and standard deviation of 4.5. Compute the following probabilities as a 4-digit decimal value or as a percent with 1-digit after the decimal. SHOW WORK and table values. a. P(X>14) b. P (12

15. Assume the random variable X is normally distributed with a mean of 22 and standard deviation of 4.5. Compute the following probabilities as a 4-digit decimal value or as a percent with 1-digit after the decimal. SHOW WORK and table values. a. P(X>14) b. P (12

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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**Statistical Probability Calculation using Normal Distribution** Welcome to our educational resource on calculating probabilities using the normal distribution. Below, you'll find an example problem that assumes a normally distributed random variable, \( X \), and teaches you how to compute certain probabilities with precision. --- **Problem Statement:** Assume the random variable \( X \) is normally distributed with a mean (\( \mu \)) of 22 and a standard deviation (\( \sigma \)) of 4.5. Your task is to compute the following probabilities, either as a 4-digit decimal value or as a percent with 1-digit after the decimal. Be sure to **SHOW WORK** and reference **table values** where necessary. --- ### Problem 15 1. **a. Probability that \( X \) is greater than 14:** Compute \( P(X > 14) \) *Table & Work Required:* - **Z-Score Calculation:** \[ Z = \frac{X - \mu}{\sigma} \] - **Table Lookup:** Use the Z-table to find the probability associated with the calculated Z-value. *Answer Box:* | Probability | |--------------| | | 2. **b. Probability that \( X \) is between 12 and 16:** Compute \( P(12 < X < 16) \) *Table & Work Required:* - **Z-Score Calculation for both limits:** \[ Z = \frac{X - \mu}{\sigma} \] - **Table Lookup:** Use the Z-table to find probabilities for both Z-values and calculate the difference. *Answer Box:* | Probability | |--------------| | | --- **Note:** Ensure you perform all calculations accurately to demonstrate understanding, referencing the standard normal distribution table for precise values. These practices are essential for mastering basic statistical concepts in probability theory. ---
Transcribed Image Text:**Statistical Probability Calculation using Normal Distribution** Welcome to our educational resource on calculating probabilities using the normal distribution. Below, you'll find an example problem that assumes a normally distributed random variable, \( X \), and teaches you how to compute certain probabilities with precision. --- **Problem Statement:** Assume the random variable \( X \) is normally distributed with a mean (\( \mu \)) of 22 and a standard deviation (\( \sigma \)) of 4.5. Your task is to compute the following probabilities, either as a 4-digit decimal value or as a percent with 1-digit after the decimal. Be sure to **SHOW WORK** and reference **table values** where necessary. --- ### Problem 15 1. **a. Probability that \( X \) is greater than 14:** Compute \( P(X > 14) \) *Table & Work Required:* - **Z-Score Calculation:** \[ Z = \frac{X - \mu}{\sigma} \] - **Table Lookup:** Use the Z-table to find the probability associated with the calculated Z-value. *Answer Box:* | Probability | |--------------| | | 2. **b. Probability that \( X \) is between 12 and 16:** Compute \( P(12 < X < 16) \) *Table & Work Required:* - **Z-Score Calculation for both limits:** \[ Z = \frac{X - \mu}{\sigma} \] - **Table Lookup:** Use the Z-table to find probabilities for both Z-values and calculate the difference. *Answer Box:* | Probability | |--------------| | | --- **Note:** Ensure you perform all calculations accurately to demonstrate understanding, referencing the standard normal distribution table for precise values. These practices are essential for mastering basic statistical concepts in probability theory. ---
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