# Question

Suppose Jack and Diane are each attempting to use simulation to describe the sampling distribution from a population that is skewed left with mean 50 and standard

deviation 10. Jack obtains 1000 random samples of size n = 3 from the population, ﬁnds the mean of the 1000 samples, draws a histogram of the means, ﬁnds the mean of the means, and determines the standard deviation of the means. Diane does the same simulation, but obtains 1000 random samples of size n = 30 from the population.

(a) Describe the shape you expect for Jack’s distribution of sample means. Describe the shape you expect for Diane’s distribution of sample means.

(b) What do you expect the mean of Jack’s distribution to be? What do you expect the mean of Diane’s distribution to be?

(c) What do you expect the standard deviation of Jack’s distribution to be? What do you expect the standard deviation of Diane’s distribution to be?

deviation 10. Jack obtains 1000 random samples of size n = 3 from the population, ﬁnds the mean of the 1000 samples, draws a histogram of the means, ﬁnds the mean of the means, and determines the standard deviation of the means. Diane does the same simulation, but obtains 1000 random samples of size n = 30 from the population.

(a) Describe the shape you expect for Jack’s distribution of sample means. Describe the shape you expect for Diane’s distribution of sample means.

(b) What do you expect the mean of Jack’s distribution to be? What do you expect the mean of Diane’s distribution to be?

(c) What do you expect the standard deviation of Jack’s distribution to be? What do you expect the standard deviation of Diane’s distribution to be?

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