1) To find the confidence interval
the sample mean x = 38 σ = 9; n = 85;
The confidence level is 95% (CL = 0.95) <span>CL = 0.95
so α = 1 – CL = 0.05
</span><span>α/2 = 0.025 </span>Z(α/2) = z0.025
The area to the right of Z0.025 is 0.025 and the area to the left of Z0.025 is 1 – 0.025 = 0.975
Z(α/2) = z0.025 = 1.645 This can be found using a computer, or using a probability table for the standard normal distribution.
<span>EBM = (1.645)*(9)/(85^0.5)=1.6058</span> x - EBM = 38 – 1.6058 = 36.3941 <span> x + EBM = 38 + 1.6058 = 39.6058
</span>The 95% confidence interval is (36.3941, 39.6058).
The answer is the letter D
<span>The value of 40.2 is <span>within the 95% confidence interval for the mean of the sample
</span></span>2) To find the confidence interval <span>
<span>the sample mean x = </span>76 σ = 20; n = 102; </span><span>
The confidence level is 95% (CL = 0.95) CL = 0.95
so α = 1 – CL = 0.05
α/2 = 0.025 Z(α/2) = z0.025
The area to the right of Z0.025 is 0.025 and the area to the
left of Z0.025 is 1 – 0.025 = 0.975
Z(α/2) = z0.025 = 1.645 This can be found using a computer,
or using a probability table for the standard normal distribution.
EBM = (1.645)*(20)/(102^0.5)=3.2575 x - EBM = 76 – 3.2575 = 72.7424 </span> x +
EBM = 76 + 3.2575 = 79.2575 <span>
The 95% confidence interval is (</span>72.7424 ,79.2575).<span>
The answer is the letter </span>A
and the letter D<span>
The value of 71.8 and 79.8 <span> are </span> outside<span>
the 95% confidence interval for the mean of the sample</span></span>
Answer:
Set 4: 12 ft, 16 ft, 20 ft
Step-by-step explanation:
A right angle triangle is a triangle in which one of the angles is a right angle (i.e 90°). The side opposite to the right angle is the longest side and is called the hypotenuse. The Pythagoras theorem for a right angle triangle states the the square of the hypotenuse is equal to the sum of the square of the remaining two sides.
For set 1:
4² + 5² = 16 + 25 = 41
6² = 36
6² ≠ 4² + 5²
It does not form a right triangle
For set 2:
8² + 12² = 64 + 144 = 208
20² = 400
20² ≠ 8² + 12²
It does not form a right triangle
For set 3:
10² + 20² = 100 + 400 = 500
30² = 900
30² ≠ 10² + 20²
It does not form a right triangle
For set 3:
12² + 16² = 144 + 256 = 400
20² = 400
20² = 12² + 16²
It forms a right triangle
Answer:
-7.7
Step-by-step explanation:
-18 divided by 7 = -2.57
-2.57 multiplied by 3 = -7.7
-7.7
I used simplistic form for this equation as the numbers where quite long.
The equation for ten times the sum of half a number and 6 is 8 would be: 10(1/2n+6)=8
AB/LM = BC/MN
8/12 = 14/MN
8(MN) = 12 * 14
8(MN) = 168
MN = 168/8
MN = 21 Hope this helps and please mark as brainliest!
