### Critical Values and Standard Normal Distribution#### Critical Values for Hypothesis TestingThe diagram at the top shows the critical values for various significance levels ($\alpha$) in one-tailed and two-tailed tests:1. **One-tailed (left) Test:** - $\alpha = 0.05$, critical z = -1.64 - $\alpha = 0.01$, critical z = -2.33 - $\alpha = 0.001$, critical z = -3.08 *The shaded area represents the critical region under the curve to the left.*2. **One-tailed (right) Test:** - $\alpha = 0.05$, critical z = 1.64 - $\alpha = 0.01$, critical z = 2.33 - $\alpha = 0.001$, critical z = 3.08 *The shaded area represents the critical region under the curve to the right.*3. **Two-tailed Test:** - $\alpha = 0.05$, critical z = ±1.96 - $\alpha = 0.01$, critical z = ±2.57 - $\alpha = 0.001$, critical z = ±3.32 *The shaded areas represent the critical regions under both tails of the curve.*#### Standard Normal TableThe table below the diagrams provides values for the cumulative distribution function of the standard normal distribution. This table allows you to find the probability that a standard normal random variable is less than or equal to a given value (Z):- The table is structured in a grid format, with Z-scores ranging from 0.0 to 2.9.- Each cell within the table represents the cumulative probability from the standard normal distribution. For example, at Z = 1.0 and 0.05, the cumulative probability is 0.5199.This information is essential for determining the probability associated with a Z-score in statistical analyses, particularly hypothesis testing and confidence interval estimation. It helps in finding critical values needed to make informed decisions in research studies. **Question 2: Potency of Antiviral Pills**A population of individual antiviral pills is measured based on their potency. The potency follows a normal distribution with:- Mean: 20 micrograms of active medicine- Standard deviation: 2 microgramsDetermine which of the following options represents the range of active medicine that includes 68% of the population of pills:a. 20 to 22 micrograms b. 19 to 21 micrograms c. 18 to 20 micrograms d. 18 to 22 micrograms e. 16 to 24 micrograms **Explanation**: The range that includes 68% of the population in a normal distribution is typically within one standard deviation from the mean.

Solution-: Let, X= The potency of individual antiviral pills Given: We find minimum and maximum…

2. A population of individual antiviral pills is measured on their potency. The potency is normally distributed with a mean of 20 micrograms of active medicine and a standard deviation of 2 micrograms. Which of the following is a minimum and a maximum level of active medicine that includes 68% of the population of pills. a. 20 to 22 micrograms b. 19 to 21 micrograms c. 18 to 20 micrograms d. 18 to 22 micrograms e. 16 to 24 micrograms

2. A population of individual antiviral pills is measured on their potency. The potency is normally distributed with a mean of 20 micrograms of active medicine and a standard deviation of 2 micrograms. Which of the following is a minimum and a maximum level of active medicine that includes 68% of the population of pills. a. 20 to 22 micrograms b. 19 to 21 micrograms c. 18 to 20 micrograms d. 18 to 22 micrograms e. 16 to 24 micrograms

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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