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IgorC [24]
3 years ago
11

No scale is shown on this map of a wilderness area. The distance between Rose Lake and the main road is 3.5 mi. On the map it is

2 in. The distance from Rose Lake to the hiking trail is 4 in. What is the actual distance in miles between Rose Lake and the hiking trail? A. 1.75 mi. B. 7 mi. C. 8 mi. D. 14 mi.
Mathematics
1 answer:
borishaifa [10]3 years ago
3 0

Answer:

7 miles.

Step-by-step explanation:

We have to set up a ratio, where x is the actual distance in miles between Rose Lake and the hiking trail.

[tex]3.5 : 2 = x : 4[tex]

[tex]2x = 3.5 * 4[tex]

[tex]2x = 14[tex]

[tex]x = 7[tex]

The actual distance between Rose Lake and the hiking trail is 7 miles.

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In a simple random sample of 300 boards from this shipment, 12 fall outside these specifications. Calculate the lower confidence
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Answer:

The 95% confidence interval for the percentage of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).

Step-by-step explanation:

In a random sample of 300 boards the number of boards that fall outside the specification is 12.

Compute the sample proportion of boards that fall outside the specification in this sample as follows:

\hat p =\frac{12}{300}=0.04

The (1 - <em>α</em>)% confidence interval for population proportion <em>p</em> is:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

The critical value of <em>z</em> for 95% confidence level is,

z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

*Use a <em>z</em>-table.

Compute the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification as follows:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.04\pm1.96\sqrt{\frac{0.04(1-0.04)}{300}}\\=0.04\pm0.022\\=(0.018, 0.062)\\\approx(1.8\%, 6.2\%)

Thus, the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).

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Step-by-step explanation:

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