## Problem 5: Statistical Analysis of a Retirement CommunityThe problem involves analyzing the ages of thousands of residents in a retirement community, which are normally distributed with a mean of 70 years and a standard deviation of 4 years.### a. Proportion of Population Between 60 and 80To find the proportion of the population between ages 60 and 80:1. Calculate the Z-scores for ages 60 and 80. - \( Z = \frac{60 - 70}{4} = -2.5 \) - \( Z = \frac{80 - 70}{4} = 2.5 \)2. Using the Z-table, determine the proportion for each Z-score. - For \( Z = -2.5 \), approximately \( 0.0062 \) (or 0.62%) - For \( Z = 2.5 \), approximately \( 0.9938 \) (or 99.38%)3. The proportion of residents between ages 60 and 80 is: - \( 0.9938 - 0.0062 = 0.9876 \) (or 98.76%)### b. Probability of Sample Mean AgeGiven that a sample of 45 residents is chosen at random:1. Calculate the Z-scores for the sample mean ages 68.5 and 71.75. - \( Z = \frac{68.5 - 70}{\frac{4}{\sqrt{45}}} \approx -2.24 \) - \( Z = \frac{71.75 - 70}{\frac{4}{\sqrt{45}}} \approx 2.92 \)The probability that the sample mean is between 68.5 and 71.75 can be determined similarly using the Z-table values for each Z-score.### c. 95% Confidence Interval for the Sample MeansThe task is to find the limits within which 95% of the possible sample mean values lie. This typically corresponds to Z-scores of -1.96 and 1.96 for a normal distribution. The interval can be calculated using these Z-scores and the standard error of the mean.Note: Handwritten corrections and calculations in red mark the numerical answers, but further numerical accuracy might require precise Z-table lookups and calculations.

Given that. X~N( μ , ?) μ=70 , ?=4 Z-score =( x - μ )/?

Answered: 2: (2>60) (2480) 5. A The ages of the…

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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A data set consists of the 11 data points shown below, plus one additional data point. When the additional point is included in the data set, the sample standard deviation of the 12 points is computed to be 15.225. If it is known that the additional data point is 25 or less, find the value of the twelfth data point. 48, 42, 12, 56, 33, 23, 24, 21, 37, 21, 27 Value of the additional data point =
4) Which of these samples would have the smallest standard deviation? a. 101, 92, 84, 131 b. -25, -10, -19, -3 с. 15, 9, 2, 21 d. 190, 187, 189, 192
6. A kinesiologist wanted to examine the effects of temperature and humidity on exercise performance. Each participant was asked to walk on a treadmill at a normal pace for 60 minutes, and the kinesiologist recorded the distance walked (miles). She assigned participants to one of 4 conditions that varied in temperature (normal or high) and humidity (normal or high). Mean distance walked by the four groups are shown in the table below. Assume a = .05 and Tukey HSD = 0.39. Normal temperature High temperature Normal humidity M = 3.00 M = 2.80 High humidity M = 2.80 M = 2.00 Complete the following conclusion: The factorial ANOVA revealed significant main effects of temperature [F (1, 24) = 25.00, p<.05] and humidity [F (1, 24) = 19.65, p<.05] and a significant Temperature x Humidity interaction [F (1, 24) = 9.25, p < .05].
6. Section 5.7 Number 46 parts b and c only 46. According to the College Board, scores on the Math SAT for the class of 2017 had a mean of 527 and a standard deviation of 107. Assume that they are roughly normally distributed. a. What was the interval spanned by the middle 50% of scores? b. What was the interval spanned by the middle 68% of scores? c. How high must a student score in order to be in the top 2.5% of scores?
16.
4. What is the standard deviation of the data {7, 1, 7, 10, 5, 3, 2}? 5.0 2.7 3.0 9.0
6
10. On a history exam, Roberto had a score of 72, which was exactly 3 standard deviations below the mean. The standard deviation for the exam is 4. a. What score was 2 standard deviations above the mean? b. What percent of the scores were at least 88? 72 c. What score represents the mean? d. What percent of the scores were between 80 and 88?
3. The following are the number of customers on a certain day in three milktea shops. Calculate the mean, mode, range, standard deviation, coefficient of variation measures. Compare its variability. milktea: 14, 15, 16, 17, 18, 19, 21 Gongcha: 22, 22, 24, 25, 28, 32, 32 Infinitea: 10, 11, 12, 12, 12, 15, 16
7. Female Pulse Rates Pulse rates of adult females are listed in Data Set 1 “Body Data” in Appendix B. The lowest pulse rate is 36 beats per minute, the mean of the listed pulse rates is x = 74.0 beats per minute, and their standard deviation is s = 12.5 beats per minute. a. What is the difference between the pulse rate of 36 beats per minute and the mean pulse rate of the females? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the pulse rate of 36 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between - 2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 36 beats per minute significant?
17. Exams I, II, and III have mean results of 67, 72, and 76, respectively, and standard deviations of 11, 8, and 5, respectively. Mary takes exam I, John takes exam II, and Sarah takes exam III. They each score 83. Rank them from lowest to highest results according to z-scores. (A) John, Sarah, Mary (C) Mary, John, Sarah (B) John, Mary, Sarah (D) Mary, Sarah, John If you feel the answer is none of the choices given, submit no answer to the question.
6

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