Mathematics, 27.08.2019 01:00 thu651777p0vibf

The owner of a restaurant is reviewing customer complaints. in a random sample of 227 complaints, 57 complaints were about the slow speed of the service. create a 95% confidence interval for the proportion of complaints that were about the slow speed of the service. use excel to create the confidence interval, rounding to four decimal places.

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Answer from: staffordkimberly

0.1375 to 0.3624

Step-by-step explanation:

Given :The owner of a restaurant is reviewing customer complaints. In a random sample of 227 complaints, 57 complaints were about the slow speed of the service.

To Find :Create a 95% confidence interval for the proportion of complaints that were about the slow speed of the service.

Solution:

n = 227

x = 57

Formula of confidence for proportion: $\widecap{p}-z_{\frac{\alpha}{2}}\sqrt{\frac{\widecap{p}\widecap{q}}{n}}$ to $\widecap{p}+z_{\frac{\alpha}{2}}\sqrt{\frac{\widecap{p}\widecap{q}}{n}}$

$\widecap{p}=\frac{x}{n}$

$\widecap{p}=\frac{57}{227}$

$\widecap{p}=0.25$

$\widecap{q}=1-\widecap{p}$

$\widecap{q}=1-0.25$

$\widecap{q}=0.75$

z at 95% is 1.96

Substitute the values in the formula :

Confidence for proportion: $0.25-1.96\sqrt{\frac{0.25 \times 0.75}{57}}$ to $0.25+1.96\sqrt{\frac{0.25 \times 0.75}{57}}$

Confidence for proportion: 0.1375 to 0.3624

Hence 95% confidence interval for the proportion of complaints that were about the slow speed of the service is 0.1375 to 0.3624

Answer from: Quest

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Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.