Question

Looking at all eruptions at the Old Faithful geyser last year, the distribution of length of eruption has a population mean of 104 seconds and population standard deviation of 6 seconds. Suppose we take record the sample mean eruption length for many random samples of 25 eruptions.

a) What is the standard deviation of the sampling distribution of the sample mean?

b) In the space below, sketch a density curve that describes that sampling distribution. Label the mean of the distribution and the values one, two, and three standard deviations away from the mean.

Using your sketch from part (b) to help you if needed, answer the following questions.

c) About what percentage of sample means would you expect to be between 101.6 and 106.4 seconds?

d) About what percentage of sample means would you expect not to be between 100.4 and 107.6 seconds?

e) Identify these statements about sampling distributions as true (T) or false (F).

____ A sampling distribution can be shown graphically using a histogram.

____ The Central Limit Theorem applies only to the distribution of population means.
The Central Limit Theorem applies only to the distribution of population means.

Answer 1

a)

The standard deviation of the sampling distribution of the sample mean is

b)

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Following is the graph:

(c)

The area between 101.6 and 106.4 is 95%. The percentage of sample means would you expect to be between 101.6 and 106.4 seconds is 95%.

(d)

The percentage of sample means would you expect to be between 100.4 and 107.6 seconds is 99.7%. So percentage of sample means would you expect not to be between 100.4 and 107.6 seconds is 1 - 0.997 = 0.003.

Answer: 0.3%

(e)

True:  A sampling distribution can be shown graphically using a histogram.

False: The Central Limit Theorem applies only to the distribution of population means.