# Cameron University Statistics Worksheet

4/10/22, 9:09 PMMyOpenMath
Chapter 7 HW
Joao Guilherme Guercheski Duleba
Question 1
0/1 pt
3
19
A population of values has a normal distribution with μ = 15.7 and σ = 41. You intend to draw a
random sample of size n = 185. Please show your answers as numbers accurate to 4 decimal places.
Find the probability that a single randomly selected value is less than 10.
P(X < 10) = Find the probability that a sample of size n = 185 is randomly selected with a mean less than 10. P(x̄ < 10) = Question 2 0/1 pt A population of values has an unknown distribution with random sample of size n = 112. μ = 36.6 and σ = 87.3 3 19 . You intend to draw a What is the mean of the distribution of sample means? (Please enter an exact answer.) μx̄ = What is the standard deviation of the distribution of sample means? (Please report your answer accurate to 2 decimal places.) σx̄ = Question 3 0/1 pt 3 19 A population of values has a normal distribution with μ = 200.3 and σ = 17.5. You intend to draw a random sample of size n = 99. Please show your answers as numbers accurate to 4 decimal places. Find the probability that a single randomly selected value is between 198.4 and 201.4. P(198.4 < X < 201.4) = Find the probability that a sample of size 201.4. P(198.4 < x̄ n = 99 is randomly selected with a mean between 198.4 and < 201.4) = Question 4 https://www.myopenmath.com/assess2/?cid=134459&aid=9586328#/print 0/1 pt 3 19 1/11 4/10/22, 9:09 PM MyOpenMath A population of values has a normal distribution with μ = 239.4 and σ = 77.2. You intend to draw a random sample of size n = 219. Please answer the following questions, and show your answers to 1 decimal place. Find P69, which is the value (X) separating the bottom 69% values from the top 31% values. P69 (for population) = Find P69, which is the sample mean (x̄) separating the bottom 69% sample means from the top 31% sample means. P69 (for sample means) = Question 5 The population mean will always be the same as the mean of all possible samples of size 23. 0/1 pt ¯ ¯¯ X 3 19 that can be computed from True False Hint: Help Question 6 0/1 pt 3 19 3 19 If a researcher wants to have a distribution of a sample that is approximately normal then that researcher should collect a sample with sample size greater than 30. True False Hint: Help Question 7 https://www.myopenmath.com/assess2/?cid=134459&aid=9586328#/print 0/1 pt 2/11 4/10/22, 9:09 PM MyOpenMath If the sample size is 64 and the population standard deviation is 40, then the standard deviation of the sampling distribution for means is 5. True False Hint: Help Question 8 0/1 pt 3 19 If the data are quantitative and there are more than 30 numbers in the data set, then the distribution of this data will always be approximately normally distributed. True False Hint: Help Question 9 0/1 pt 3 19 If the distribution of the population is bimodal, then the sampling distribution for the sample means for this population with sample size 50 will be unimodal. True False Hint: Help Question 10 https://www.myopenmath.com/assess2/?cid=134459&aid=9586328#/print 0/1 pt 3 19 3/11 4/10/22, 9:09 PM MyOpenMath A larger sample size will result in a smaller sample standard deviation for the sample. True False Hint: Help Question 11 0/1 pt 3 19 3 19 When using the central limit theorem for means with n = 94, it is not necessary to assume the distribution of the population data is normally distributed. True False Hint: Help Question 12 https://www.myopenmath.com/assess2/?cid=134459&aid=9586328#/print 0/1 pt 4/11 4/10/22, 9:09 PM MyOpenMath Suppose the mean starting salary for nurses is \$65,509 nationally. The standard deviation is approximately \$10,762. The starting salary is not normally distributed but it is mound shaped. A sample of 49 starting salaries for nurses is taken. State the random variable. Starting salary for a nurse. The mean starting salary of a nurse. The standard deviation of starting salaries of nurses. What is the mean of the sample mean? μx̄ = What is the standard deviation of the sample mean? Round to two decimal places. σx̄ = What is the shape of the sampling distribution of the sample mean? Why? You can say the sampling distribution of the sample mean is not normally distributed since the sample size is greater than 30. You can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is greater than 30. You can say the sampling distribution of the sample mean is normally distributed since the sample size is greater than 30. Find the probability that the sample mean is more than \$73,000. Round to four decimal places. P(x̄ > 73000) =
Find the probability that the sample mean is less than \$55,000. Round to four decimal places.
P(x̄ < 55000)= If you did find a sample mean of more than \$73,000 would you find that unusual? What could you conclude? It is not unusual to find a sample mean more than \$73,000, since the probability is at least 5%. If you find a sample mean more than \$73,000, then it may indicate that the population mean has not changed. It is not unusual to find a sample mean more than \$73,000, since the probability is less than 5%. If you find a sample mean more than \$73,000, then it may indicate that the population mean has not changed. It is unusual to find a sample mean more than \$73,000, since the probability is at least 5%. If you find a sample mean more than \$73,000, then it may indicate that the population mean has changed. It is unusual to find a sample mean more than \$73,000, since the probability is less than 5%. If you find a sample mean more than \$73,000, then it may indicate that the population mean has changed. https://www.myopenmath.com/assess2/?cid=134459&aid=9586328#/print 5/11 4/10/22, 9:09 PM MyOpenMath Question 13 0/1 pt 3 19 According to the New York State Board of Law Examiners, approximately 62% of people taking the New York Bar Exam passed the exam. 1. If 10 people who have taken the New York Bar Exam are randomly selected, what is the probability that at least 79% have passed? Round your answer to 4 decimal places. 2. If 40 people who have taken the New York Bar Exam are randomly selected, what is the probability that at least 79% have passed? Round your answer to 4 decimal places. 3. Why did the probability decrease? The probability decreased since the sample size decreased resulting in a wider distribution which increased the area of the right tail. The probability decreased since the sample size increased resulting in a narrower distribution which reduced the area of the right tail. Question 14 https://www.myopenmath.com/assess2/?cid=134459&aid=9586328#/print 0/1 pt 3 19 6/11 4/10/22, 9:09 PM MyOpenMath Labor force participation among women rose in the United States between 1975 and 2000 and has beeen declining ever since. According to the U.S. Bureau of Labor Statistics, 55% of women were in the labor force in 2015. 1. If 80 working age women are randomly selected, what is the probability that between 52% and 62% are in the labor force? Round your answer to 4 decimal places. 2. If 190 working age women are randomly selected, what is the probability that between 52% and 62% are in the labor force? Round your answer to 4 decimal places. 3. Why did the probability increase? The probability increased since the sample size increased and the distribution of sample proportions is more spread out. The probability increased since the sample size increased and the sample proportions are more concentrated near the true labor force participation rate of 55 % . Question 15 0/1 pt 3 19 If 15% of adults in a certain country work from home, what is the probability that fewer than 48 out of a random sample of 400 adults will work from home? (Round your answer to 3 decimal places) Question 16 https://www.myopenmath.com/assess2/?cid=134459&aid=9586328#/print 0/1 pt 3 19 7/11 4/10/22, 9:09 PM MyOpenMath According to a survey, 10% of Americans are afraid to fly. Suppose 1,100 Americans are sampled. a. What is the probability percentage that 121 or more Americans in the survey are afraid to fly? Round the percent to two decimal places. b. What is the probability percentage that 165 or more Americans in the survey are afraid to fly? Round the percent to two decimal places. c. What is the probability percentage that 8% or less of the Americans surveyed answered they were afraid to fly? Round the percent to two decimal places. Question Help: Video Question 17 0/1 pt 3 19 In an effort to cut costs and improve profits, any US companies have been turning to outsourcing. In fact, according to Purchasing magazine, 54% of companies surveyed outsourced some part of their manufacturing process in the past two to three years. Suppose 555 of these companies are contacted. a. What is the probability percentage that 338 or more companies outsourced some part of their manufacturing process in the past two or three years? Round the percent to two decimal places. b. What is the probability percentage that 285 or more companies outsourced some part of their manufacturing process in the past two or three years? Round the percent to two decimal place. c. What is the probability percentage that 48% or less of these companies outsourced some part of their manufacturing process in the past two or three years? Round the percent to two decimal places. Question 18 0/1 pt A random sample of size n = 645 from a population whose parameter is p = 0.22 3 19 . a. What is the mean of the distribution of sample means? Round the answer accurate to 2 decimal places. b. What is the standard deviation of the distribution of sample means? Round the answer accurate to 2 decimal places. Question Help: Video https://www.myopenmath.com/assess2/?cid=134459&aid=9586328#/print 8/11 4/10/22, 9:09 PM Question 19 https://www.myopenmath.com/assess2/?cid=134459&aid=9586328#/print MyOpenMath 0/1 pt 3 19 9/11 4/10/22, 9:09 PM MyOpenMath According to a survey, 10% of Americans are afraid to fly. Suppose 1,100 Americans are sampled. Preliminary: a. Is it safe to assume that n ≤ 0.05 of all subjects in the population? Yes No b. Verify np(1 − p) ≥ 10. np(1 − p) = Problem: Suppose we are interested in the probability percentage that 121 or more Americans in the survey are afraid to fly. a. What is the point estimate? Round to two decimal places. p̂ = b. Draw a figure by shading the region that corresponds to the scenario given the z-score is z = 1.1. Shade: Left of a value . Click and drag the arrows to adjust the values. -1.5 c. What is the probability percentage that 121 or more Americans in the survey are afraid to fly? Round the percent to two decimal places. % d. Interpret the probability found in part c. in context of Americans that are afraid to fly. Write one complete sentence in order to earn full credit. https://www.myopenmath.com/assess2/?cid=134459&aid=9586328#/print 10/11 4/10/22, 9:09 PM https://www.myopenmath.com/assess2/?cid=134459&aid=9586328#/print MyOpenMath 11/11

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