The answer is 270. Brainliest answer?
The probability is 1 in 36 because there are 36 possible rolling combinations.
Using the z-distribution, it is found that the 90% confidence interval for the true proportion of club members who use compost is (0.392, 0.508).
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
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 estimate and the sample size are given by:
![\pi = 0.45, n = 200](https://tex.z-dn.net/?f=%5Cpi%20%3D%200.45%2C%20n%20%3D%20200)
Hence, the bounds of the interval are:
![\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 - 1.645\sqrt{\frac{0.45(0.55)}{200}} = 0.392](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.45%20-%201.645%5Csqrt%7B%5Cfrac%7B0.45%280.55%29%7D%7B200%7D%7D%20%3D%200.392)
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 + 1.645\sqrt{\frac{0.45(0.55)}{200}} = 0.508](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.45%20%2B%201.645%5Csqrt%7B%5Cfrac%7B0.45%280.55%29%7D%7B200%7D%7D%20%3D%200.508)
More can be learned about the z-distribution at brainly.com/question/25890103
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This one is going to i
hope this helped
After 4 years
the value = 1000 × (1.1)⁴
the value = 1000 × 1.4641
the value = 1464.1