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.

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

Pictured 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 = 30.Based on the histograms, what is the most likely value of the population mean? 0.5 3.0 4.5 7.5 350

Question 6Typically the x-axis of a bar graph shows1 pointfrequency.the values of the variable of interest.percent.the distribution.