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Lorico [155]
3 years ago
11

If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most avera

ges for the lengths of pregnancies in the sample?
Mathematics
1 answer:
Alexeev081 [22]3 years ago
6 0

Answer:

The range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

Step-by-step explanation:

The complete question is:

The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 17 days. If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?

Solution:

As the sample size is large, i.e. <em>n</em> = 47 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean by the normal distribution.

So,\bar X\sim N(\mu,\ \frac{\sigma^{2}}{{n}})

The range of the middle 98% of most averages for the lengths of pregnancies in the sample is the 98% confidence interval.

The critical value of <em>z</em> for 98% confidence level is,

<em>z</em> = 2.33

Compute the 98% confidence interval as follows:

CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}

     =267\pm 2.33\cdot\frac{17}{\sqrt{47}}\\\\=267\pm5.78\\\\=(261.22, 272.78)\\\\\approx (261, 273)

Thus, the range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

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