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…

Answered: State the Central Limit Theorem. Choose…

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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Recall that Benford's Law clalms that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a v leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millons of numbers in a large computer data bank. You draw a random sample of n = 229 numbers from this file and r 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. large data file, the probability of getting a number with "1" as the () Test the dalm that p is more than 0.301. Use a 0.10. (a) what is the level of signifcance? State the null and alternate hypotheses. O Hg: p = 0.301; H p> 0.301 O Hgi P = 0.301; Hip 0.301; Hp- 0.301 O Ho: P= 0.301; H: p- 0.301 (b) what sampling distribution will you use? O The Student's t, since np > 5 and ng > 5. O The…
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 pulse rates of 155 randomly selected adult males vary from a low of 41 bpm to a high of 113 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 95% 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 = (Round up to the nearest whole number as needed.)
A random sample of n = 260 measurements is drawn from a binomial population with probability of success 0.75. Complete parts a throughc below. a. Find E(p) and oA. p The mean of the sampling distribution of p is 0.75 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. O A. The shape of the sampling distribution of p is approximately uniform because the sample size is large. O B. The shape of the sampling distribution of p is approximately normal because the sample size is smal. O C. The shape of the sampling distribution of p is approximately uniform because the sample size is small. O D. The shape of the sampling distribution of p is approximately normal because the sample size is large. c. Find P (p< 0.8) The probability that p is less than 0.8 is (Round to four decimal places as needed.)
3. For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n= 65 and p = 0.7 a. Normal approximation is not suitable. b. Normal approximation is suitable.
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?
5.79 Suppose x is a binomial random variable with p = 4 and n = 25. NW
For the population whose distribution is Uniformly distributed from 30 to 52, random samples of size n = 39 are repeatedly taken. Compute u and round to two decimals. Use this value to find the following. Round answers to three decimals if needed. Answers of 0 and 1 are possible due to rounding. a. P(40 < < 43): b. The 25th percentile for sample means: Submit Question
a sample is selected from a normal population with u=40 and σ =12. If the sample mean of M=36 corresponds to z=-2.00, then the sample size is n=64. is it true or false
For the population whose distribution is Uniformly distributed from 35 to 45, random samples of size n = 34 are repeatedly taken. Compute u and round to two decimals. Use this value to find the following. Round answers to three decimals if needed. Answers of 0 and 1 are possible due to rounding. a. P(41 < a < 43): b. The 15th percentile for sample means: Submit Question r
Random samples of size n = 2 are drawn from a finite population consisting of the numbers 5,6,7,8, and 9. Find the mean of the population µ. b. Find the standard deviation of the population o. Find the mean of the sampling distribution of the sample means µg. d. Find the standard deviation of the sampling distribution of the sample а. С. means og. e. Verify the Central Limit theorem by: Comparing u and µg. Comparing o and og. I. II.

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