Select 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.

1.  The distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough. 
2.  The distribution is normal regardless of the sample size, as long as the population distribution is normal. 
3.  The distribution’s is the same as the population mean. 
4.  The distribution’s standard deviation is smaller than the population standard deviation. 

Question 2

Select one answer. 

10 points

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?

1.  0.5
2.  3.0
3.  4.5
4.  7.5
5.  350

Question 3

Select one answer. 

10 points

Suppose that a candy company packages a bag of jelly beans whose weight is supposed to be 30 grams, but in fact, the weight varies from bag to bag according to a normal distribution with mean μ = 30 grams and standard deviation σ = 3 grams.

If the company sells the jelly beans in packs of 9 bags, what can we say about the likelihood that the average weight of the bags in a randomly selected pack is 2 or more grams lighter than advertised?

1.  There is about a 16% chance of this occurring. 
2.  It is extremely unlikely for this to occur; the probability is very close to 0. 
3.  There is about a 5% chance of this occurring. 
4.  There is no way to evaluate this likelihood, since the sample size (n = 9) is too small.
5.  There is about a 2.5% chance of this occurring. 

Question 4

Select all that apply. 

10 points

In which of the following scenarios would the distribution of the sample mean x-bar be normally distributed? Check all that apply.

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