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 =
population SD = ![\frac{7.4}{\sqrt[]{463} }](https://tex.z-dn.net/?f=%5Cfrac%7B7.4%7D%7B%5Csqrt%5B%5D%7B463%7D%20%7D)
= 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.
Answer:
S_6 = 252
Step-by-step explanation:
We are told that the 10th, 4th and 1st term of an A.P are three consecutive terms of a G.P.
Now,formula for nth term of an AP is;
a_n = a + (n - 1)d
Thus;
a_10 = a + (10 - 1)d
a_10 = a + 9d
Also;
a_4 = a + (4 - 1)d
a_4 = a + 3d
First term is a.
Thus, since they are consecutive terms of a G.P, it means that;
(a + 9d)/(a + 3d) = (a + 3d)/a
Cross multiply to get;
a(a + 9d) = (a + 3d)(a + 3d)
a² + 9ad = a² + 6ad + 9d²
a² will cancel out to give;
9ad - 6ad = 9d²
3ad = 9d²
Divide both sides by 3d to get;
a = 3d
We are told that the first term is 4.
Thus, 4 = 3d
d = 4/3
We saw earlier that ratio of the GP is (a + 3d)/a
Thus; r = (4 + 3(4/3))/4 = 8/4 = 2
Sum of n terms of a G.P is given by;
S_n = a(rⁿ - 1)/(r - 1)
S_6 = 4(2^(6) - 1)/(2 - 1)
S_6 = 252
Answer:
Its just 1.
Step-by-step explanation:
anything to the power of 0 is 1 simple
Answer:
u can maybe help it depends on the questions
Answer:
19.4 miles per gallon
Step-by-step explanation:
In this question, we are asked to calculate the distance traveled per gallon of fuel filled into a tank. Hence, this looks like a rate question.
Firstly, we need to know the distance covered during the duration in which the fuel was in the engine. To do this, we subtract the final odometer reading from the initial odometer reading. This is mathematically equal to: 24,923.4 - 24,583.9 = 339.5 miles.
This means she travelled a total distance of 339.5 miles on the 17.5 gallon fuel.
Hence, the miles per gallon gotten by the van is numerically equal to 339.5/17.5 = 19.4 miles/ gallon
