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Mean birthweight is studied because low birthweight is an indicator of infant mortality. A study of babies in Norway published in the International Journal of Epidemiology shows that birthweight of full-term babies (37 weeks or more of gestation) are very close to normally distributed with a mean of 3600 g and a standard deviation of 600 g. Suppose that Melanie is a researcher who wishes to estimate the mean birthweight of full-term babies in her hospital. What is the minimum number of babies should she sample if she wishes to be at least 90% confident that the mean birthweight of the sample is within 200 grams of the the mean birthweight of all babies? Assume that the distribution of birthweights at her hospital is normal with a standard deviation of 600 g.

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Answer:

Step-by-step explanation:

Let X represent the birthweight of infant.

X is N(3600, 600)

To get within 200 gms from the mean

we must have x lying in (3400, 3800)

Let sample size be n

For this sample, sample mean is N(3600, 600/sqrt n)

For 90% confidence about the mean weight fromstd normal distribution we find that

z = ±1.645

So margin of error = 1.645*std error =200

[tex]1.645*\frac{600}{\sqrt{n} } <200\\\sqrt{n} >3*1.645\\n >25[/tex]

Atleast 25 numbers should beconsidered.

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