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mote1985 [20]
3 years ago
8

The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are r

andom variables that follow a normal distribution with a variance of 0.16.
Determine the interval of 95% confidence for the average heights of the population.
Mathematics
1 answer:
Dimas [21]3 years ago
4 0

Answer:

The 95% confidence interval for the average heights of the population is between 1.7108m and 1.7892m.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

The standard deviation is the square root of the variance. So

\sigma = \sqrt{0.16} = 0.4

Then

M = 1.96*\frac{0.4}{\sqrt{400}} = 0.0392

The lower end of the interval is the mean subtracted by M. So it is 1.75 - 0.0392 = 1.7108m

The upper end of the interval is the mean added to M. So it is 1.75 + 0.0392 = 1.7892m

The 95% confidence interval for the average heights of the population is between 1.7108m and 1.7892m.

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