Question

Please explain, in basic terms, how the Central Limit Theorem helps me obtain a likely value of the population mean from just one sample.  In addition to a detailed explanation, a couple of examples would be helpful.  Thanks.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Statistics

Related Statistics Q&A

Find answers to questions asked by students like you.

Q: How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complet...

A: Sample mean = 97 oC.Standard deviation, sigma is 17 oC.The sample size, n is 58.

Q: How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complet...

A: a)Given:

Q: skipping lunch- A nutritionist wishes to determine, within 3%, the true proportion of adults who do ...

A: It is given that margin of error (E) is 0.03 and the confidence level is 95%.

Q: The mean amount of time it takes a kidney stone to pass is 13 days and the standard deviation is 4 d...

A: It is given that the mean and standard deviation are 13 and 4.

Q: Please show TI 84 steps. We don't use standardized table for z score

A: Introduction:According to the Central Limit Theorem, if the sampling distribution of the sample prop...

Q: From a sample with n=32, the mean number of televisions per household is 4 with a standard deviation...

A: Chebyshev’s rule can be used for the large set data. It says that at least 1-1/k2 percentage of the ...

Q: Please show TI 84 steps

A: According to the provided data, the sample size, n is 1100 with the probability of success, p is 0.8...

Q: Problem 6

A: In a multiple linear regression model, an explanatory variable is said to be most important if it ha...

Q: In 2008, the Detroit Lions set an NFL record by losing all 16 regular season games. Suppose that the...

A: It is given that n =16.Here, probability of winning an individual game is 0.10.

Q: Find the area of the shaded region. The graph depicts the standard normal distribution of bone densi...

A: The area of the shaded region is given byP(Z>-1.08) = 1-P(Z≤-1.08)P(Z≤-1.08) = 0.14 (From Excel =...

Q: make up 2 data sets, each with 5 values, that have the same mean and median, but different standard ...

A: Let the two datasets be x and y

Q: Question 1 At a local university, a sample of 49 evening students was selected in order to determine...

A: The hypotheses are given below:

Q: #4: Suppose that X1,... , X7n is an i.i.d. random sample drawn from a U[a, 1] uniform distribution, ...

A: Click to see the answer

Q: Please show TI 84 steps

A: Computation of mean and standard deviation:Here, n=300; p̂=0.40; q̂=0.60 (=1−0.40).The mean and stan...

Q: Intensive care units (ICUs) generally treat the sickest patients in a hospital. ICUs are often the m...

A: From the given information,The average length of stay in ICU is 3.9 days, so μ = 3.9

Q: The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed b...

A: Given sample size of black coffee cups n = 50Caffeine content mean = 110mgStandard deviation = 7.1 m...

Q: Will you show me step by step how to solve this?

A: Here two z values are required to be calculated.Given:P(|Z|>zo) = 0.056It could be simplified as:

Q: Sam computed a 90% confidence interval for μ from a specific random sample of size n. He claims that...

A: Sam computed a 90% confidence interval for µ from a specific random sample of size n.

Q: The US population is 13% African American.  If you were to take a SRS of 500 Americans, what is the ...

A: It is given that the sample size n is 500 and p hat = 0.13.

Q: PBS News Hour reported in 2014 that 39.4% of Americans between the ages of 25 and 64 have at least a...

A: It is given that n =55 and p = 0.3940.The probability mass function of binomial distribution is give...

Q: 4. In which of the following cases OLS estimation of Healthcare=a+bAge+u will be biased? a) Only inc...

A: Explanation:A random sample helps avoid unnecessary bias.Random errors, such as random typing errors...

Q: In a state's Pick 3 lottery, you pay $1.48 to select a sequence of three digits (from 0 to 9), such ...

A: Given Total number of picks in lottery = 3Total number of digits from 0 to 9 = 10The amount paid to ...

Q: Problem 3

A: Preliminary calculation:Using the EXCEL formula “=NORM.S.INV(1-(0.05/2))”, the z-value for 95% confi...

Q: How many different three-letter words (including nonsense words) can be formed such that the two let...

A: The permutation can be used to find the number of ways by which a set of objects can be arranged whe...

Q: 63% of all students at a college still need to take another math class. If 4 students are randomly s...

A: It is given that n =4 and p = 0.63.The probability mass function of binomial distribution is given b...

Q: A history class has 75 members. If there is a 12% absentee rate per class meeting, find the mean, va...

A: It is given that n is 75 and p is 0.12.

Q: At their​ inauguration, the ages of the first six​ (out of a current number of​ 45) presidents of a ...

A: Mean:The formula for finding mean is shown below:

Q: Big babies: The National Health Statistics Reports described a study in which a sample of 355 one-ye...

A: a) From the given information, the claim of the problem is testing whether the mean weight of one-ye...

Q: 29. Surgical complications : A medical researcher wants to construct a 99% confidence interval for t...

A: It is given that margin of error (E) is 0.04 and the confidence level is 99%.

Q: Compute the critical value Zα/2 that corresponds to an 82​% level of confidence.   Zα/2 = ​(Rou...

A: It is given that the level of confidence is 0.82.

Q: A fruit retailer complains to a wholesaler that 60 percent of the boxes of apples shipped to the ret...

A: Given:X: Number of boxes contain rotten applen: Sample size = 15p: Proportion of the boxes of apples...

Q: The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 120 a...

A: Given dataMean = 120Standard Deviation = 23Calculating the z-value corresponding to 30th percentile ...

Q: Bags of dog food are labeled 1 through 50. What is the probability that the dog will choose a number...

A: It is provided that, the bags of food have been labeled through 1 to 50.The formula to calculate the...

Q: What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of err...

A: Given confidence interval 95%.maximal margin of error = 0.1.The critical Z score for 95% confidence ...

Q: Please show TI 84 steps

A: It is given that mean is 10, level of significance is 0.05 and the sample size is 14.From the altern...

Q: Please show TI 84 steps

A: Note:Hey, since there are multiple sub-parts question posted, we will answer first three sub-parts. ...

Q: Assume the random variable X has a binomial distribution with the given probability of obtaining a s...

A: Given Datan = 9p = 0.5Required probability is given by

Q: The Student Monitor surveys 1200 undergraduates from 100 colleges semiannually to understand trends ...

A: Consider X be a random variable which follows normal distribution indicating the time spent per week...

Q: According to the Center for Disease Control and Prevention (CDC), the mean life expectancy in 2015 f...

A: It is given that the mean is 71.8, the population standard deviation is 15, sample size is 100 and t...

Q: Statistics Question

A: Hypotheses:Denote μ1, μ2 as the true average number of days spent in the hospital for childbirth, by...

Q: Please See Picture

A: X- be the winnings when we quit.Case-1 win in first spinProbability of win in first spin = 18/38prof...

Q: Please see picture

A: Part a) 

Q: Suppose that 30% of all students who have to buy a text for a particular course want a new copy (the...

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are sol...

Q: The article "Facebook Use and Academic Performance Among College Students"† estimated that 87% perce...

A: It is given that the population proportion is 0.87. In the survey the sample proportion van be obtai...

Q: How many ways are there to choose first, second, and third prizes in an art contest with 18 entries?

A: Introduction:According to the permutation rule, if r distinct items are to be chosen from n items wi...

Q: Find the standard deviation of the distribution in the following situations. (a) MENSA is an organiz...

A: a)It is given that the mean is 100.The IQs in the top 2% of the population represents the area of 0....

Q: A poll asked the question, "What do you think is the most important problem facing this country toda...

A: Solution:The confidence interval formula for proportion formula is,

Q: Explain the four different types of sampling and give an example of each.

A: Different types of sampling methods with examples.Types of random samplings(1) Simple random samplin...

Q: Part 1 The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overlo...

A: Part 1: Consider M be a mean for a random variable of sample size, n equal to 4689. Since the sample...

Q: Question 3 of 7 Game consoles: A poll surveyed 341 video gamers, and 109 of them said that they pref...

A: It is given that in the survey, it is found that 109 out of 341 video gamers said that they prefer p...