A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployedis 25 weeks. Assume that the length of unemployment is normally distributed with population mean of 25 weeks and thepopulation standard deviation of 9 weeks. Suppose you would like to select a random sample of 35 unemployedindividuals for a follow-up study. Round the answers of following questions to 4 decimal places.a. What is the distribution of X? X ~ N(b. What is the distribution of a? a ~ N(c. What is the probability that one randomly selected individual found a job less than 27 weeks?d. For 35 unemployed individuals, find the probability that the average time that they found the next job is less than27 weeks.e. For part d), is the assumption of normal necessary? ONo O Yes

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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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Suppose that the heights of adult men in the United States are normally distributed with a mean of 71 inches and a standard deviation of 3 inches. What proportion of the adult men in the United States are more than 6 feet tall? (Hint: 6 feet = 72 inches.) Round your answer to at least four decimal places. 0 X
The mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5,400. The distribution of incomes is skewed to the right. For samples of size 111 determine whether the distribution of x is normal or approximately normal and give its mean and standard deviation. O A. Normal, mean p; = $28,520, standard deviation o; = $5,400 O B. Approximately normal, mean p: = $28,520, standard deviation o: = $513 OC. Approximately normal, mean p- = $28,520, standard deviation o = $5,400 O D. Normal, mean p- = $28,520, standard deviation o- = 513
A set of data items is normally distributed with a mean of 108 and a standard deviation of 27. Convert each of the following data items to a z- score. Round your answer to the nearest hundredth. (a) 226 Z = (b) 85 Z =
The distribution of the number of motor vehicles per household in the United States (the population) and sampling distributions of the mean for samples of size 4 and 10 are shown in below. A.Which distribution is which? Make a rough estimate of the mean and standard deviation of each distribution. Explain the reasons of your choices.b. The mean of the population is about 1.7. Theoretically, what is the mean of the sampling distribution for samples of size 4? Of size 10? Are these computed means consistent with your estimates of the means in the histograms? Briefly explain.c. The standard deviation of the population is about 1. Theoretically, what is the Standard Error (SE) of the sampling distribution for samples of size 4? Of size 10? Are these computed SEs consistent with your estimates of the SEs in the histograms? Briefly explain.d. Compare the shapes of the three distributions. Are the shapes consistent with the Central Limit Theorem? Briefly explain.
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 30 weeks. Assume that the length of unemployment is normally distributed with population mean of 30 weeks and the population standard deviation of 7 weeks. Suppose you would like to select a random sample of 36 unemployed individuals for a follow-up study. Round the answers of following questions to 4 decimal places. a. What is the distribution of X? X - N( 30 b. What is the distribution of ? N( 30 c. What is the probability that one randomly selected individual found the next job is less than 31 weeks? 7 or or d. For 36 unemployed individuals, find the probability that the average time that they found the next job is less than 31 weeks. e. For part d), is the assumption of normal necessary? Yes No o
Your favorite statistics professor is starting up a UNO Genius Club, and you really want to get in. Everyone enrolled at UNO is eligible to take the qualifying exam and 8,647 students take the exam. You show up to take the test on a Sunday morning. Your professor announces on Monday that the distribution of scores was normal with a mean test score of 120 and a standard deviation of 14. Answer questions 24-28 using this information. What percentage of students scored above 112? **Don’t round z scores while calculating; round final answer to 2 decimals. 1) draw the normal curve, 2) plot the z-scores, and 3) shade in the area of interest.
You are given the following information: sample mean is equal to 103.55, population standard deviation is equal to 14.88, sample size is equal to 111 and the national average is equal to 109. What would be the value of z-observed?
Exhibit 9-41 A random sample of 9 students selected from the student body of a high school had an average age of 14 years. We want to determine if the average age of all the students at the high school is significantly different from 13. Assume the distribution of the population of ages is normal with a standard deviation of 1 year. Refer to Exhibit 9-41. What is the p-value for this test? 0.00135 0.0027 1.96 0.0045

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