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valentina_108 [34]
3 years ago
6

Twenty-five wooden beams were ordered or a construction project. The sample mean and he sample standard deviation were measured

xbar = 190cm, s = 5cm. Calculated confidence interval for the mean is [188.29; 191.71].
Which confidence level was chosen? Assume distribution to be normal.
A. 99%
B. 90%
C. 95%
D. 99.9%
Engineering
1 answer:
aksik [14]3 years ago
4 0

Answer:

Correct option: B. 90%

Explanation:

The confidence interval is given by:

CI = [\bar{x} - z\sigma_{\bar{x}} , \bar{x}+z\sigma_{\bar{x}} ]

If \bar{x} is 190, we can find the value of z\sigma_{\bar{x}}:

\bar{x} - z\sigma_{\bar{x}}  = 188.29

190 - z\sigma_{\bar{x}}  = 188.29

z\sigma_{\bar{x}}  = 1.71

Now we need to find the value of \sigma_{\bar{x}}:

\sigma_{\bar{x}} = s / \sqrt{n}

\sigma_{\bar{x}} = 5/ \sqrt{25}

\sigma_{\bar{x}} = 1

So the value of z is 1.71.

Looking at the z-table, the z value that gives a z-score of 1.71 is 0.0436

This value will occur in both sides of the normal curve, so the confidence level is:

CI = 1 - 2*0.0436 = 0.9128 = 91.28\%

The nearest CI in the options is 90%, so the correct option is B.

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