Answer:
A. 12.68 - 14.72 hours
B. Normal distribution.
Step-by-step explanation:
Part A
This question is using quantitative data. A 99% confidence interval means that you want to know the range where 99% of the population will be. To find this you have to convert the 99% CI into the z-score which is -2.58SD to + 2.58SD.
Note that the standard deviation(SD) is from the sample, not the population. We still need to find the standard deviation of the population. The formula is:
population SD = ![\frac{o}{\sqrt[]{n} }](https://tex.z-dn.net/?f=%5Cfrac%7Bo%7D%7B%5Csqrt%5B%5D%7Bn%7D%20%7D)
Where the o= sample SD = 7.4
n= number of sample = 463
The calculation will be:
population SD = ![\frac{o}{\sqrt[]{n} }](https://tex.z-dn.net/?f=%5Cfrac%7Bo%7D%7B%5Csqrt%5B%5D%7Bn%7D%20%7D)
population SD =
= 0.3951
The bottom limit will be:
Mean - SD * z-score= 13.7 - 0.3951*2.58 = 12.68 hours
The upper limit will be:
Mean + SD * z-score= 13.7 + 0.3951*2.58 =14.72 hours
The 99% CI range will be 12.68 - 14.72 hours
Part B
The table used to convert confidence interval into z-score depends on the distribution type of the data. Most data is classified as normal distributed, a data type that will concentrated at mean and spread equally from the mean. Normal distribution data will look like a bell which make it also called bell curve.
The question tells you that the data is normal distribution, but that doesn't mean every data is normally distributed. There are a lot of other data distribution type so we have to do some tests to know the normality of the data in real-life data.
The distance of x : 9 - 1 = 8
the distance of y : 18 - 12 = 6
To get a total distance
you can use the formula → √( x^2 + y^2 )
So the answer is √( 8^2 + 6^2 ) = √( 64 + 36 )
= √100 = 10
Answers from top to bottom:
(0,-6)
(-1,0)
(-1,-6)
(0,0)
Explanation:
The rule you use is
when it comes to 180 degree rotations (either clockwise or anticlockwise/counterclockwise). So we flip the signs of the x and y coordinates. Any point on an axis will stay on the same axis. The origin is the intersection of the two axes, so this point does not move at all. We call this point fixed or stationary. The fixed point is one where every point rotates around it.
You will find the area the square and then find out what 4/5 of that area is.
A = bh
6 cm x 6 cm
A = 36 square cm
4/5 of 36 square cm
4/5 x 36
28 4/5 square cm
The area of the rhombus is 28 4/5 square cm. Use this to solve for the height of the rhombus.
A = bh
<u>28 4/5</u> = <u>6 x h</u>
6 6
h = 4 4/5 cm
The height of the rhombus is 4 4/5 cm.