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The last person didn't answer this question and only drew a graph. 11. The length of...

The last person didn't answer this question and only drew a graph.

11.

The length of human pregnancies from conception to birth is, on average, 266 days with a standard deviation of 16 days. Enough medical study has been done on this variable that we know it follows an approximate normal distribution.

Suppose all possible samples of size 50, taken from the recorded lengths of pregnancies, are drawn and the mean is found for each resulting sample. Describe the shape and scaling on the graph of the resulting sampling distribution for the sample mean values. Hint: Apply the Central Limit Theorem!

Math   Statistics-And-Probability   
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Answer #1

The answer to this question will be a plot itself, which is normally distributed. There is nothing to solve here.

Using Central Limit Theorem, if we draw repeated samples of size 50 from the population , and find the mean of each of these samples, and plot these means, the means will be distributed Normally. The distribution would be expected to be centred at 266 which is the population mean.

Standard error of Sampling distribution would be 16/√50=2.26

Bell shaped

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