State the Central Limit Theorem.Choose the correct answer below.A. For a random sample of n observations selected from a population with mean μ and standard deviation o, when n is sufficiently large, the sampling distribution of x will be approximately aOnormal distribution with mean μ = μ and standard deviation=ox= √nB. For a random sample of n observations selected from a population with mean μ and standard deviation o, when n is sufficiently large, the sampling distribution of x will be a uniformOdistribution with mean μ = μ and standard deviation =XnO C. For a random sample of n observations selected from a population with mean µ and standard deviation o, when n>4, the sampling distribution of x will be exactly a normal distribution withOmean μ = μ and standard deviation o- =X√nD. For a random sample of n observations selected from a population with mean μ and standard deviation o, when n is sufficiently large, the sampling distribution of x will be approximately anormal distribution with mean μ = μ and standard deviationox= 0.

Central limit theorem:-A random sample of n observations selected from the population with mean μ…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2. Suppose that X1, X2, X3 and X4, are independent and identically distributed with a mean of 2.5 and a standard deviation of 0.6. Find the mean and standard deviation for variables Y and W defined below. Let Y= 4X1 а. b. Let W= Xi + X2 + X3 + X4
Solve for numbers 4 and 5
Population 1 is Normally distributed with a mean of 40 and a standard deviation of 4, and population 2 is normally distributed with a mean of 25 and a standard deviation of 7. Suppose we select independent SRSS of n1 = 100 and n2 = 85 from population 1 and 2 respectively. Which of the following are the values of the mean and the standard deviation of the sampling distribution of T1 – F2? 4(1 4) O 65, 7(1 7) 100 85 72 42 O 15. 100 85 4(1-4) O 15, 7(1-7) 100 85 42 O 15. 100 85 V馬-VE 42 72 65, 100 85
The annual salary for one particular occupation is normally distributed, with a mean of about $122,000 and a standard deviation of about $22,000. Random samples of 34 are drawn from this population, and the mean of each sample is determined. Find the mean and standard deviation of the sampling distribution of these sample means. Then, sketch a graph of the sampling distribution.
Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ=12.3. Assume the population is normally distributed.
Calculate N and M for the following frequency distribution. X Frequency2 53 34 45 86 117 9 What are the median and mode for the frequency distribution in Q1? If a sample has a SX (sum of X) = 35 and N=7, what is the mean? Calculate N and M for the following frequency distribution. X Frequency2 93 45 89 312 218 4 What are the median and mode for the frequency distribution in Q4? If a sample has a SX (sum of X) = 56 and M=7, what is the sample size (N)? Calculate N and M for the following frequency distribution. X Frequency2 33 65 79 2What are the median and mode for the frequency distribution in Q7? If a sample has aN=16andM=4.5, what was theSX (sum of X)
The pulse rates of 158 randomly selected adult males vary from a low of 44 bpm to a high of 120 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 90% confidence that the sample mean is within 2 bpm of the population mean. Complete parts (a) through (c) below. a. Find the sample size using the range rule of thumb to estimate σ. n=245 b. Assume that σ=10.5 bpm, based on the value s=10.5 bpm from the sample of 158 male pulse rates. n= c.. Compare the results from parts (a) and (b). Which result is likely to be better?
A random sample of n = 78 measurements is drawn from a binomial population with probability of success 0.2. Complete parts a through d below. a. Give the mean and standard deviation of the sampling distribution of the sample proportion, p. The mean of the sampling distribution of p is The standard deviation of the sampling distribution of p is (Round to four decimal places as needed.) b. Describe the shape of the sampling distribution of p. OA. The shape of the sampling distribution of p is approximately normal because the sample size is large. OB. The shape of the sampling distribution of p is approximately uniform because the sample size is large. OC. The shape of the sampling distribution of p is approximately normal because the sample size is small. OD. The shape of the sampling distribution of p is approximately uniform because the sample size is small. c. Calculate the standard normal'z-score corresponding to a value of p = 0.32. The standard normal z-score corresponding to a…
A variable of a population has a mean of μ=100 and a standard deviation of σ=42 a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean ____ and standard deviation ____ b. For part (a) to be true, what assumption did you make about the distribution of the variable under consideration?A. Normal distribution.B. No assumption was made.C. Uniform distribution. c. Is the statement in part (a) still true if the sample size is 16 instead of 49? Why or why not?A. No, the sampling distribution of the sample mean is never normal for sample size less than 30.B. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.C. Yes, the sampling distribution of the sample mean is always normal.
The annual salary for one particular occupation is normally distributed, with a mean of about $124,000 and a standard deviation of about $16,000. Random samples of 30 are drawn from this population, and the mean of each sample is determined. Find the mean and standard deviation of the sampling distribution of these sample means. Then, sketch a graph of the sampling distribution.
It is estimated that 90% of all 19-year-old men have weights ranging from 117 to 207 lb. Assuming the weight distribution can be adequately modeled by a normal curve and that 117 and 207 are equidistant from the average weight µ, calculate σ.
A random sample of size 10 yielded roughly "mound-shaped" data with a sample mean of 63.5 and a sample variance of 60.8. Let (L, OU) be the interval estimate that contains the population mean with 95% probability. Find the width of the interval. That is, find 0 – 0₁. 4.52 5.49 5.58 5.70 9.04 10.99 11.16 11.40 none of the other answers give the correct width

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