**The Overhead Reach Distances of Adult Females**The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.9 cm. Consider the following problems related to the distribution of reach distances:### a. Find the probability that an individual distance is greater than 212.50 cm.- **Solution:** - The probability is [ ]. - *(Round to four decimal places as needed.)*### b. Find the probability that the mean for 20 randomly selected distances is greater than 198.70 cm.- **Solution:** - The probability is [ ]. - *(Round to four decimal places as needed.)*### c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?- **Solution:** - Choose the correct answer below: - ⃝ A. The normal distribution can be used because the finite population correction factor is small. - ⃝ B. The normal distribution can be used because the probability is less than 0.5. - ⃝ C. The normal distribution can be used because the original population has a normal distribution. - ⃝ D. The normal distribution can be used because the mean is large.This exercise encourages understanding of normal distribution and its application in statistical problems involving continuous data. Make sure to apply appropriate statistical techniques and formulas to find the solutions and understand the reasoning behind using normal distribution for different sample sizes.

Given X=212.50 Mean=200 Standard deviation=8.9

Answered: a. Find the probability that an…

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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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 61 ounces and a standard deviation of 7 ounces.a) 95% of the widget weights lie between and b) What percentage of the widget weights lie between 54 and 75 ounces? %c) What percentage of the widget weights lie above 40 ? %
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A sampling distribution of a sample mean is normal only if the population is normal. Choose the correct answer below. O A. The statement is false. A sampling distribution of a sample mean is approximately normal if either n ≥ 30 or the population is normal. B. The statement is false. A sampling distribution of a sample mean is never normal. O C. The statement is false. A sampling distribution of a sample mean is approximately normal only if n ≥ 30. OD. The statement is true.
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The average final exam score for the statistics course is 82%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 90, 78, 82, 59, 67, 71, 64, 78, 67, 57, 79, 86, 66, 56 What can be concluded at the the αα = 0.05 level of significance level of significance? For this study, we should use (t-test for a population mean, z-test for a population proportion) The null and alternative hypotheses would be: H0: (symbol) (symbol) ____ H1: (symbol) (symbol) ____ The test statistic (?,t,z) = ____ (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is (symbol) αα Based on this, we should (accept, reject, fail to reject) the null hypothesis.…
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Suppose the true population proportion is p = 0.5. The figure below shows the distribution of the sample proportion (p) values for 3 different sample sizes, n = 20, n=100 and n=500. 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8
ne A small warehouse employs a supervisor at $1350 a week, an inventory manager at $800 a week, six stock boys at $420 a week, and four drivers at $520 a week. nts a) Find the mean and median wage. k The mean wage is $. ch The median wage is $. ntent b) How many employees earn more than the mean wage? an c) Which measure of center best describes a typical wage at this company, the mean or the median? Resou se O A. The median best describes the typical wage. The mean is not a good measure of center because it is affected by the two higher salaries. O B. The median best describes the typical wage. The mean is not a good measure of center because it is affected by the multitude of duplicate salaries. ible Res O C. The mean best describes the typical wage. The median is not a good measure of center because it is affected by the multitude of duplicate salaries, se ase Opti OD. The mean best describes the typical wage. The median is not a good measure of center because it is affected by the…
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