The text displayed in the image is as follows:"Which theorem states that, for large n, the sampling distribution of the sample mean is approximately \(N \left( \mu, \frac{\sigma}{\sqrt{n}} \right)\) for any population with mean \(\mu\) and finite standard deviation \(\sigma\)."This text refers to the Central Limit Theorem, which is a fundamental concept in statistics. The theorem explains that, regardless of the original distribution of the data, the distribution of the sample mean will tend to be normal if the sample size is sufficiently large. The parameters \( \mu \) and \( \sigma \) represent the mean and standard deviation of the population, respectively, while \( n \) is the sample size.There are no graphs or diagrams associated with this text.

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Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Airlines tend to overbook their flights because they assume a certain percentage of people will be 'no shows' due to change in plans or late connecting flights. A recent study suggested that 86% of people actually show up for their flight on time. A random sample of 222 booked passengers is taken and whether or not they showed up on time is recorded for each of them. The Central Limit Theorem for proportions says that the sampling distribution of the proportion of people who show up on time for their flight will have a Normal shape. (a) Give the center and standard error for the sampling distribution of proportions. Round to four decimal places as needed. mean = and standard error = (b) What is the probability that at least 88% of the randomly selected booked passengers showed up on time? P(ˆp ≥0.88)= (c) What is the probability that between 82% and 90% of the randomly selected booked passengers showed up on time? P(0.82≤ˆp ≤0.9)= (d) Is 83% an unusually low percentage of…
Suppose a simple random sample of size n= 125 is obtained from a population whose size is N = 20,000 and whose population proportion with a specified characteristic is p = 0.4. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Approximately normal because ns0.05N and np(1- p) 2 10. O B. Approximately normal because ns0.05N and np(1- p) < 10. O C. Not normal because ns0.05N and np(1- p) 2 10. O D. Not normal because ns0.05N and np(1 - p)< 10. Determine the mean of the sampling distribution of p. = (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. =(Round to six decimal places as needed.) (b) What is the probability of obtaining x= 55 or more individuals with the characteristic? That is, what is P(p20.44)? P(p20.44) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 40 or…
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4. Suppose two independent random samples of size n1 = n2 = 10 are from a normal population. Assume the population variances are equal. Determine a cutoff k such that P>k) - 0.05 where S, and S2 are the respective sample standard deviations.
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Which theorem states that, for large n, the sampling distribution of the sample mean is approximately N H, for any population with mean u and finite standard deviation o.