Using the z-distribution, a sample size of 180 is needed for the estimate.
<h3>What is a z-distribution confidence interval?</h3>
The confidence interval is:
![\overline{x} \pm z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%5Cpm%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
The margin of error is given by:
![M = z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which:
is the sample mean.
is the standard deviation for the population.
In this problem, we have a 98% confidence level, hence
, z is the value of Z that has a p-value of
, so the critical value is z = 2.327.
The population standard deviation is of
, and to find the sample size, we have to solve for n when M = 4.
Hence:
![M = z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
![4 = 2.327\frac{23}{\sqrt{n}}](https://tex.z-dn.net/?f=4%20%3D%202.327%5Cfrac%7B23%7D%7B%5Csqrt%7Bn%7D%7D)
![4\sqrt{n} = 2.327 \times 23](https://tex.z-dn.net/?f=4%5Csqrt%7Bn%7D%20%3D%202.327%20%5Ctimes%2023)
![\sqrt{n} = \frac{2.327 \times 23}{4}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B2.327%20%5Ctimes%2023%7D%7B4%7D)
![(\sqrt{n}) = \left(\frac{2.327 \times 23}{4}\right)^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%20%3D%20%5Cleft%28%5Cfrac%7B2.327%20%5Ctimes%2023%7D%7B4%7D%5Cright%29%5E2)
n = 179.03.
Rounding up, as a sample size of 179 would result in an error slightly above 4, a sample of 180 is needed.
More can be learned about the z-distribution at brainly.com/question/25890103
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I think it’d be 2 and 3 if you’re rounding 2.984
Answer:
5
Step-by-step explanation:
Answer:
85t
Step-by-step explanation:
1. Volume of a cone: 1. V = (1/3)πr2h 2. Slant height of a cone: 1. s = √(r2 + h2) 3. Lateral surface area of a cone: 1. L = πrs = πr√(r2 + h2) 4. Base surface area of a cone (a circle): 1. B = πr2 5. Total surface area of a cone: 1. A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))
hope this helps
Answer:
First three terms:
22,24,26
There are 15 terms in the sequence that are 50 or less, yet only 14 if its just less than 50.