Using the z-distribution, it is found that the 90% confidence interval is given by: (0.6350, 0.6984).
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:

In which:
is the sample proportion.
In this problem, we have a 90% confidence level, hence
, z is the value of Z that has a p-value of
, so the critical value is z = 1.645.
The sample size and the estimate are given by:

Hence, the bounds of the interval are given by:


The 90% confidence interval is given by: (0.6350, 0.6984).
More can be learned about the z-distribution at brainly.com/question/25890103
#SPJ1
Girls: 81
boys: 75
4x +6 = 156
4x = 150
x = 37.5
2x = 75
girls: 75 + 6
boys: x
Answer: The height is 6.07 meters
Step-by-step Explanation: The distance between the elevator and the bottom of the barn is given as 9 meters. Also for the hay elevator to move bales of hay to the second story of the barn lift it makes an angle of elevation of 34 degrees with the ground. With these we can derive a right angled triangle with the reference angle as 34 degrees, the side facing it which is the height or h (opposite) is yet unknown, and the side between the reference angle and the right angle (adjacent) is 9. We shall apply the trigonometric ratio as follows;
Tan 34 = opposite/adjacent
Tan 34 = h/9
0.6745 = h/9
0.6745 x 9 = h
6.0705 = h
Therefore the approximate height of the barn to the ground is 6.07 meters