### 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

See similar textbooks

Similar questions

Answer all questions: 1. What is the range and standard deviation for the following population of scores? Scores: 5,2,5,4
2. The scores from a state standardized test have a mean of 200 and a standard deviation of 50. The distribution of the scores is roughly bell shaped. The percentage of scores that lie between 100 and 300 is approximately a. 34% b. 47.5% c. 50% d. 68% e. 95%
Researchers collected information on the body parts of a new species of frog. The thumb length for the female frog has a mean of 8.28 mm and a standard deviation of 0.78 mm. Let x denote thumb length for a female specimen. a. Find the standardized version of x. b. Determine and interpret the z-scores for thumb lengths of 10.3 mm and 7.1 mm. Round your answers to two decimal places. a. Find the standardized version of x. z=enter your response here
Help The mean useful life of car batteries is 48 months. They have a standard deviation of 5. Assume the useful life of batteries is normally distributed. a. Calculate the percent of batteries with a useful life of less than 43 months. (Round your answer to the nearest hundredth percent.) b. Calculate the percent of batteries that will last longer than 53 months. (Round your answer to the nearest hundredth percent.) a. Percent of batteries % b. Percent of batteries Next > Mc Graw Hill ! 1 Q A @ 2 Ne N r option W #3 S % So E X command $ 4 D R C < Prev % LO 5 F T 14 of 14 6 V G ⠀⠀ Y & 7 #Y H B 4 8 Dal J N 1 K M O Save & Exit L < MOSISO . command H Submit 96 1 ? optic
Q) The RATES of a SWEET BOX follows a normal distribution with a mean of $2.20 and a standard deviation of $0.20. Find the RATE for which 10.23% of sweet boxes are exceeded. Round your answer to nearest cent (hundredth) if necessary.
The incomes of trainees at a local mill are normally distributed with a mean of $1,100 and a standard deviation of $150. What percentage of trainees earn more than $1,300 a month? Group of answer choices 9.18% 40.82% 90.82% 35.31%