According to one study, brain weights of men are normally distributed with a mean of 1.10 kg and a standard deviation of 0.12 kg. Use the data to answer parts (a) through (e).[Links to view two pages of the table of areas under the standard normal curve]**a. Determine the sampling distribution of the sample mean for samples of size 3. Interpret your answer in terms of the distribution of all possible sample mean brain weights for samples of three men.**- The mean of the sample mean is \( \mu_{\bar{x}} = \_\_ \) kg. (Type an integer or a decimal. Do not round.)- The standard deviation of the sample mean is \( \sigma_{\bar{x}} = \_\_ \) kg. (Round to four decimal places as needed.)Interpret these answers in context.For [blank space to enter value] the [dropdown menu] brain weights have a normal distribution with a mean of [blank space to enter value] kg and a standard deviation of [blank space to enter value] kg.(Type integers or decimals rounded to four decimal places as needed.)**b. Repeat part (a) for samples of size 12.**- The mean of the sample mean is \( \mu_{\bar{x}} = \_\_ \). (Type an integer or a decimal. Do not round.)- The standard deviation of the sample mean is \( \sigma_{\bar{x}} = \_\_ \). (Round to four decimal places as needed.)Interpret these answers in context.For [blank space to enter value] the [dropdown menu] brain weights have a normal distribution with a mean of [blank space to enter value] kg and a standard deviation of [blank space to enter value] kg. The image outlines a statistical exercise on brain weights of men, which are normally distributed with a mean of 1.10 kg and a standard deviation of 0.12 kg. It involves constructing graphs based on these distributions and analyzing sampling errors.The image is divided into the following sections:- **Textual Information**: - A brief introduction describes the normal distribution of men’s brain weights with specified mean and standard deviation. - Links for additional resources on the standard normal curve are provided.- **Task (c)**: - Participants are asked to construct a graph of the normal population distribution and two sampling distributions for brain weights. The task is to choose the correct graph from four options labeled A, B, C, and D. - **Graph Options**: - Each graph shows the population distribution ('Pop') and sampling distributions for different sample sizes (n = 3 and n = 12). - All graphs have a horizontal axis marked at 1.1 (the mean brain weight). - The distributions vary slightly in their spread indicated by different line types (solid for population, dotted lines for samples of size 3 and 12).- **Task (d)**: - Participants must determine the percentage of samples (n = 3) with mean brain weights within 0.1 kg of the population mean of 1.10 kg. - Instructions prompt the use of sampling error terminology, asking to round answers to two decimal places and compare the sampling error between sample sizes.The exercise is designed to illustrate the concept of sampling distribution and its relation to sample size, affecting the spread of data and the accuracy of statistical estimations.

According to a study, the brain weight of men is Normally distributed with a mean of 1.10 kg and a standard deviation of 0.12 kg.The sample average of sample size n is defined as X¯=1n∑i=1nXi, which is normally distributed. The mean of the sample average is μX¯=EX¯=E1n∑i=1nXi=1n∑i=1nEXi=1n∑i=1n1.10=1n×n×1.10.=1.10 and the sample standard deviation is σX¯=VarX¯=Var1n∑i=1nXi=1n2Var∑i=1nXi=1n2∑i=1nVarXi=1n∑i=1n0.122=1nn×0.122=1n0.12 Hence, the sample mean follows Normal distribution with a mean μX¯=1.10 and standard deviation σX¯=0.12n.a. Given the sample size n=3. The mean of the sample mean is μX¯=1.10 kg. The standard deviation of the sample mean is σX¯=0.123=0.0693 Hence, the standard deviation of the sample mean is σX¯=0.0693. Therefore, For the sample size n=3, the sample average of the brain weight of men has a Normal distribution with a mean of 1.10 kg and a stan0dard deviation of 0.0693 kg.b. Given the sample size n=12. The mean of the sample mean is μX¯=1.10 kg. The standard deviation of the sample mean is σX¯=0.1212=0.0346 Hence, the standard deviation of the sample mean is σX¯=0.0346. Therefore, For the sample size n=12, the sample average of the brain weight of men has a Normal distribution with a mean of 1.10 kg and a standard deviation of 0.0346 kg.c. The graph of the population Normal distribution with a mean of 1.10 kg and a standard deviation of 0.12 kg and the sample average for sample size n=3 follows a Normal distribution with a mean of 1.10 kg and a standard deviation of 0.0693 kg, the sample average for sample size n=12 follows a Normal distribution with a mean of 1.10 kg and a standard deviation of 0.0346 kg is Black line represents the population distribution, Blue line represents the sample distribution for sample size n=3, Red line represents the sample distribution for sample size n=12. Therefore the correct option is C. Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.

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one study, bDrain weig men are ormally distributed wiLI kg and dala to answer parts (a) Click here to view page 1 of the table of areas under the standard normal curve, Click here to view page 2 of the table of areas under the standard normal curve. a. Determine the sampling distribution of the sample mean for samples of size 3. Interpret your answer in terms of the distribution of all possible sample mean brain weights for samples of thre The mean of the sample mean is µ =O kg. (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o: = kg. (Round to four decimal places as needed.) Interpret these answers in context. For V the V brain weights have a normal distribution with a mean of kg and a standard deviation of kg. (Type integers or decimals rounded to four decimal places as needed.) b. Repeat part (a) for samples of size 12. The mean of the sample mean is u: =: (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o; = (Round to four decimal places as needed.)

one study, bDrain weig men are ormally distributed wiLI kg and dala to answer parts (a) Click here to view page 1 of the table of areas under the standard normal curve, Click here to view page 2 of the table of areas under the standard normal curve. a. Determine the sampling distribution of the sample mean for samples of size 3. Interpret your answer in terms of the distribution of all possible sample mean brain weights for samples of thre The mean of the sample mean is µ =O kg. (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o: = kg. (Round to four decimal places as needed.) Interpret these answers in context. For V the V brain weights have a normal distribution with a mean of kg and a standard deviation of kg. (Type integers or decimals rounded to four decimal places as needed.) b. Repeat part (a) for samples of size 12. The mean of the sample mean is u: =: (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o; = (Round to four decimal places as needed.)

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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