**Problem 6: Normal Distribution Analysis**A normal distribution has a mean (\(\mu\)) of 60 and a standard deviation (\(\sigma\)) of 18. For each of the following samples, compute the z-score for the sample mean (M), and indicate whether the sample mean is a typical, representative value or an extreme value for a sample of this size.a. \(M = 67\) for \(n = 4\) scores b. \(M = 67\) for \(n = 36\) scores---**Instructions:**1. **Calculate the Standard Error (SE):** The standard error is calculated as \(\sigma / \sqrt{n}\).2. **Compute the Z-score:** The z-score is calculated as \((M - \mu) / \text{SE}\).3. **Interpret the Z-score:** Determine if the sample mean is typical or extreme by considering the magnitude of the z-score.---This exercise helps in understanding the concept of sampling distribution and the interpretation of z-scores in the context of normal distribution.

(a) Given that, μ=60σ=18M=67n=4 The z-score for the sample mean (M) is, Hence, the z-score for the…

Answered: 6. A normal distribution has a mean of…

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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An SRS of 25 recent birth records at the local hospital was selected. In the sample, the average birth weight was x = 119.6 ounce Suppose the standard deviation is known to bes = 6.5 ounces. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with mean m. Based on the 25 recent birth records, the sampling distribution of the sample mean x can be represented by: a. N(119.6, 1.30). b. N(119.6, 6.5). O c. N(m, 1.30). O d. N(m, 6.5).
1. For a normal distribution, find the percent of scores that lie between the scores having z values of z = -4 and z = 6
The finite population correction is most useful for which of the following? a. It adjusts the estimated mean when the sample size is a large fraction of the population size. b. It adjusts the standard error of the mean when the sample size is a small fraction of the population size. c. It adjusts the estimated mean when the sample size is a small fraction of the population size. d. It adjusts the standard error of the mean when the sample size is a large fraction of the population size.
This assignment is worth 1 points. The extra point will be added to your overall course grade. For example: if you receive an 88% in the course you can receive up to 1 point giving you a new score of 89%. The following rubric will be used. 0.25 point for drawing the normal distribution curve with the mean value labeled on the curve and the appropriate area shaded. 0.25 point for determining the value of the standard deviation of the sample mean. 0.5 point for finding the correct probability. All work must be shown in order to receive any credit. Please upload your completed assignment here. The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours. A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours.
6. a normal distribution has a mean of 65 and an SD of 20. For each of the following samples, compute the z score for the sample mean and determine whether the mean is typical or extreme. (calculate a Z STATISTIC) I a. M=74 for a sample of 4 scores B.M=74 for a sample of 25 scores 8: F2 *3 # E D 80 F3 C 54 4 R F a V % 5 F5 T G 6 B MacBook Air Y H 87 & FEB 27 N U N 00 8 J DII M ( 9
12. A population forms a normal distribution with a mean of u = 55 and a standard deviation of o = 12. For each of the following samples, compute the z-score for the sample mean. a. M = 58 for n = 4 scores %3D b. M 58 for n = 16 scores c. M = 58 for n = 36 scores

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