<h2>
Answer with explanation:</h2>
a) Given : Sample size of students : n =1123
Number of students read above the eighth grade level = 888
Then, Number of students read at or below the eighth grade level =1123-888=235
Then , the sample proportion of tenth graders reading at or below the eighth grade level.:
![\hat{p}=\dfrac{235}{1123}=0.209260908281\approx0.209](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7B235%7D%7B1123%7D%3D0.209260908281%5Capprox0.209)
Since, the best estimate for the population proportion is the sample proportion.
Thus, the estimated proportion of tenth graders reading at or below the eighth grade level = 0.209
b) Significance level : ![\alpha= 1-0.90=0.10](https://tex.z-dn.net/?f=%5Calpha%3D%201-0.90%3D0.10)
Critical value : ![z_{\alpha/2}=1.675](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D1.675)
Confidence level for population proportion:-
![\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.209\pm (1.645)\sqrt{\dfrac{0.209(1-0.209)}{1123}}\\\\=0.209\pm0.0199589370751\\\\\approx 0.209\pm0.020=(0.189,0.229)](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%5Cpm%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cdfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%5C%5C%5C%5C%3D0.209%5Cpm%20%281.645%29%5Csqrt%7B%5Cdfrac%7B0.209%281-0.209%29%7D%7B1123%7D%7D%5C%5C%5C%5C%3D0.209%5Cpm0.0199589370751%5C%5C%5C%5C%5Capprox%200.209%5Cpm0.020%3D%280.189%2C0.229%29)
Hence, the 90% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level = (0.189,0.229)
I'm pretty sure its 30quarts.
Step-by-step explanation: if you find out how many quarts are in 3/4 gallon and multiply that bye 10 then you get your answer.
Answer:
a. 1/(2^n)
b. ¾
Step-by-step explanation:
a. Given that there are n variables in a compound proposition.
Each of the n variables have exactly two possible equally likely truth values that can be assigned.
The values are true or false.
And the value can only be either true or false at any given time
True(1) + False (1) = 2 truth values
So, the probability of each possible assignment of truth values to the n variables is 1/(2^n)
b. Given that a clause is in disjunctive form of exactly two distinct variables
n = 2 distinct variables; n = 2
1/(2^n) becomes
1/2²
= ¼
This means that there's exactly 1 combination out of possible 2² that will lead to the clause being false.
The probability that a given clause is true, given the random assignment of truth values from part (a) is calculated as 1 - ¼
= ¾
-2f is the answer I’m pretty sure