Answer:
The 95% confidence interval of the proportion of all adults that have high blood pressure is 0.17059 < 
< 0.314695
Step-by-step explanation:
The confidence interval for a proportion is given by the following formula;
Where:
x = 33
n = 136
= x/n = 33/136 = 0.243
z value for 95% confidence is 1.96
Plugging in the values, we have;
Which gives;
0.17059 < < 0.314695
Hence the 95% confidence interval of the proportion of all adults that have high blood pressure = 0.17059 < < 0.314695
From the above we have;
23.2 < x < 42.798
Since we are dealing with people, we round down as follows;
23 < x < 42.
The correct answer is the second choice.
Paolo made an error when he cross multiplied the proportion. He should have multiplied the 3 and the 8 and also the 12 and the x.
The second line should be:
12x = 24
Answer:
A.
Step-by-step explanation:
Point B on the ground is 5 cm from point E at the entrance to Ollie's house.
Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.
The complete question is as follows:
Ollie has installed security lights on the side of his house that is activated by a sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m, and the distance from B to C is 6m. Angle ACB is 15°.
The objective of this information is:
- To find angle CAB and;
- Find the distance Ollie is from the entrance to his house when he first activates the sensor.
The diagrammatic representation of the information given is shown in the image attached below.
Using cosine rule to determine angle CAB, we have:
Here:
∠CAB = Sin⁻¹ (0.3451)
∠CAB = 20.19⁰
From the diagram attached;
- assuming we have an imaginary position at the base of Ollie Standing point called point F when Ollie first activates the sensor;
Then, we can say:
∠CBD = ∠GBF
∠GBF = (CAB + ACB)
(because the exterior angles of a Δ is the sum of the two interior angles.
∠GBF = 15° + 20.19°
∠GBF = 35.19°
Using the trigonometric function for the tangent of an angle.
BF = 2.55 m
Finally, the distance of Ollie║FE║ from the entrance of his bouse is:
= 5 - 2.55 m
= 2.45 m
Therefore, we can conclude that Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.
Learn more about exterior angles here:
