The number of girls in the 14 newborn babies selected is a binomially distributed random variable with n = 14 and p = 0.5. And we know that the binomial probability distribution is given by
P(X = k) = (nCk) p^k (1–p)^(n-k)
So, P(X = 0) = (14C0) • 0.5^0 • (1–0.5)^(14-0) = 0.000
P(X = 1) = (14C1) • 0.5^1 • (1–0.5)^(14–1) = 0.001
And so on.
Thus, P(X = 4) = (14C4) • 0.5^(4 • (1–0.5)^(14–4) = 0.061
So the probability of selecting exactly 4 girls is 0.061.
Answer:
Step-by-step explanation:
From the given information;
The null hypothesis & alternative hypothesis:
![\mathbf{H_o:\mu = 2} \\ \\ \mathbf{H_1 : \mu \ne 2}](https://tex.z-dn.net/?f=%5Cmathbf%7BH_o%3A%5Cmu%20%3D%202%7D%20%20%5C%5C%20%5C%5C%20%20%5Cmathbf%7BH_1%20%3A%20%5Cmu%20%5Cne%202%7D)
The test statistics can be computed as:
![Z = \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cdfrac%7B%5Coverline%20x%20-%20%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![Z = \dfrac{2.025- 2}{\dfrac{0.07}{\sqrt{35}}}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cdfrac%7B2.025-%202%7D%7B%5Cdfrac%7B0.07%7D%7B%5Csqrt%7B35%7D%7D%7D)
![Z = \dfrac{0.025}{\dfrac{0.07}{\sqrt{35}}}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cdfrac%7B0.025%7D%7B%5Cdfrac%7B0.07%7D%7B%5Csqrt%7B35%7D%7D%7D)
![Z =2.11](https://tex.z-dn.net/?f=Z%20%3D2.11)
The p-value = 2(Z > 2.11) since this is a two-tailed test
The p-value = 2( 1 - Z < 2.11)
The p-value = 2 (1 -0.9826)
The p-value = 2 (0.0174)
The p-value = 0.0348
Decision Rule: To reject the
if the p-value is less than ![\mathbf{H_o}](https://tex.z-dn.net/?f=%5Cmathbf%7BH_o%7D)
Conclusion: We fail to reject
and conclude that the population mean = 2, thus the machine is properly adjusted.
First problem:
x 8
--- = ---
3 12
Then 12x = 24, and x = 2 (answer).
Please be fair to other students needing help. Present just one problem at a time.
Answer:
16
Step-by-step explanation:
25% of 64 were votes in favor.
25% × 64
1/4 × 64 = 64/4 = 16
16 votes were in favor.
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Long division is a step-by-step method for doing division on paper
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