The distribution of total body protein in healthy adult men is approximately Normal, with mean 12.3 kg and standard deviation 0.1 kg. If you take a random sample of 25 healthy adult men, what is the probability that their average total body protein is between 12.25 and 12.35 kg?

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Quizplus · Accepted Answer

The distribution of the sample mean for total body protein will also be normal with mean $ \mu = 12.3 $ kg and standard deviation $ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{0.1}{\sqrt{25}} = 0.02 $ kg. Using the standard normal distribution, we calculate the Z-scores for 12.25 kg and 12.35 kg: $ Z_{12.25} = \frac{12.25 - 12.3}{0.02} = -2.5 $ and $ Z_{12.35} = \frac{12.35 - 12.3}{0.02} = 2.5 $. Looking up these Z-scores in the standard normal distribution table or using a calculator, the probability of being between these Z-scores is approximately 0.9876.

The Distribution of Total Body Protein in Healthy Adult Men