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Elina [12.6K]
3 years ago
5

How do I solve this problem

Mathematics
1 answer:
Flura [38]3 years ago
3 0
Shaded is 8.67
Circle A= pir^2
A= 3.14(4)(4)
A= 50.24

Hexagon
A= 1/2ap
1/2(4)(2sqrtof3)(6)
A= 41.569

50.24-41.569=8.671


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Answer:

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

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We have a sample of executives, of size n=160, and the proportion that prefer trucks is 26%.

We have to calculate a 95% confidence interval for the proportion.

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The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.26*0.74}{160}}\\\\\\ \sigma_p=\sqrt{0.0012}=0.0347

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

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Then, the lower and upper bounds of the confidence interval are:

LL=p-z \cdot \sigma_p = 0.26-0.068=0.192\\\\UL=p+z \cdot \sigma_p = 0.26+0.068=0.328

The 95% confidence interval for the population proportion is (0.192, 0.328).

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

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