In which of the following scenarios would the distribution of the sample mean x-bar be normally distributed? Check all that apply. We take repeated random samples of size 10 from a population of unknown shape. We take repeated random samples of size 15 from a population that is normally distributed. We take repeated random samples of size 50 from a population of unknown shape. We take repeated random samples of size 25 from a population that of unknown shape.

Which of the following statements about the sampling distribution of the sample mean, x-bar, is true? Check all that apply. The distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough. The distribution is normal regardless of the sample size, as long as the population distribution is normal. The distribution's mean is the same as the population mean. The distribution's standard deviation is smaller than the population standard deviation.

Sampling Distributions Checkpoint 2Question 1Select all that apply.10 pointsWhich of the following statements about the sampling distribution of the sample mean, x-bar, is true? Check all that apply. The distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough. The distribution is normal regardless of the sample size, as long as the population distribution is normal. The distribution's mean is the same as the population mean. The distribution's standard deviation is smaller than the population standard deviation.Question 2Select one answer.10 pointsPictured below (in scrambled order) are three histograms. One of them represents a population distribution. The other two are sampling distributions of x-bar: one for sample size n = 5 and one for sample size n = 40.Based on the histograms, what is the most likely value of the population mean? 290 1 8 5Question 3Select one answer.10 pointsSuppose that a candy company makes a candy bar whose weight is supposed to be 50 grams, but in fact, the weight varies from bar to bar according to a normal distribution with mean μ = 50 grams and standard deviation σ = 2 grams.If the company sells the candy bars in packs of 4 bars, what can we say about the likelihood that the average weight of the bars in a randomly selected pack is 4 or more grams lighter than advertised? There is no way to evaluate this likelihood, since the sample size (n = 4) is too small. There is about a 16% chance of this occurring. There is about a 2.5% chance of this occurring. It is extremely unlikely for this to occur; the probability is very close to 0. There is about a 5% chance of this occurring.Question 4Select one answer.10 pointsWhen the population is not normally distributed, the sampling distribution of the mean approximates which of the following? A distribution that is not normal A slight positive skew A normal distribution given a large enough sample A normal distribution

Suppose we take repeated random samples of size 20 from a population with a mean of 60 and a standard deviation of 8. Which of the following statements is true about the sampling distribution of the sample mean (x̄)? Check all that apply. The distribution is normal regardless of the shape of the population distribution, because the sample size is large enough. The distribution will be normal as long as the population distribution is normal. The distribution's mean is the same as the population mean 60. The distribution's standard deviation is larger than the population standard deviation of 8.

A variable X is described by a semi-circular density curve with mean 0 and standard deviation 0.4, as shown below:We take a simple random sample of 1000 individuals from the semi-circular distribution and calculate the sample mean x ̄(x-bar). The sampling distribution of X ̄(x-bar) is:Question 6Answera.semi-circular with mean 0 and standard deviation 0.0126.b.semi-circular with mean 0 and standard deviation 0.004.c.approximately normal with mean 0 and standard deviation 0.004.d.approximately normal with mean 0 and standard deviation 0.4.e.approximately normal with mean 0 and standard deviation 0.0126.

You draw 10 samples (n=100) out of a population of 1000 people. If the sample mean of one of the samples is very different from the population mean, does this means this sample should not be analyzed?Question 1Answera.Trueb.FalseClear my choiceQuestion 2Not yet answeredMarked out of 1.00Flag questionTipsQuestion textFrom the distribution of a random variable X a random sample of size n is drawn. What is the distribution of ?Answer:A. normally distributedB. C.  a and bQuestion 2Answera.Ab.Bc.CClear my choiceQuestion 3Not yet answeredMarked out of 1.00Flag questionTipsQuestion textWhen you can apply the Central Limit Theorem, what does it tell us?Question 3Answera.population distribution is normally distributed.b.sampling distribution is normally distributed.c.population standard deviation is known.Clear my choiceQuestion 4Not yet answeredMarked out of 1.00Flag questionTipsQuestion textFrom the distribution of a random variable X a random sample of size n is drawn. What does x̄ represent?Question 4Answera.meanb.sample meanc.standard deviationClear my choiceQuestion 5Not yet answeredMarked out of 1.00Flag questionTipsQuestion textWhat does the law of large number say?Question 5Answera.as the sample size gets larger, the sample mean gets closer and closer to the population mean.b.as the sample size gets larger, the distribution of the sample means approaches a normal distributionc.a &b