Stat sampling distribution

Dr. Virginia Apgar developed a test of infant health that is now known as the Apgar test. It evaluates an infant's health on a scale from 0 to 10 across five different indicators - the best possible overall score is 10 on the test. Here's the distribution of Apgar scores based on over 50,000 birth records:

Suppose that we took random samples of 9 infants from this population and calculated the sample mean Apgar score X' of the infants in each sample.

Which graph shows the most reasonable approximation of the sampling distribution of X'?

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A customer service department monitors how long their callers wait on hold before being helped. The time spent by the callers on hold follows a normal distribution similar to the above graph.

Suppose that we took random samples of 15 callers and calculated the sample mean time spent on hold for each sample customers. We can assume that the callers in each sample are independent.

What would be the shape of the sampling distribution of the sample mean?

• Skewed to the left

• Skewed to the right

• Approximately normal

• Unknown: we don't have enough information to determine the shape

Serge was curious if a sample third quartile [or Q3] was an unbiased estimator of a population third quartile, He started with a large normally distributed population of test scores whose third quartile was Q3 = 80 points.

He then took a random sample of 6 tests and calculated the third quartile of the sample. He replaced those tests and repeated this process for a total of 40 trials. His results are summarized in the dotplot below, Where each dot represents the third quartile from a sample of 6 tests.

Based on these results, does sample third quartile appear to be a biased or unbiased estimator of population third quartile?

Hint the population third quartile is 80.

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Select from the options below

• Skewed to the left

• Skewed to the right

• Approximately normal

• Uniform

Each distributions used the same scale.

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