Find the mean and standard deviation for each binomial random variable:
1 answer:
Answer: a) Mean = ![=37.80](https://tex.z-dn.net/?f=%3D37.80)
Standard deviation=![=1.9442](https://tex.z-dn.net/?f=%3D1.9442)
b) Mean = ![56.00](https://tex.z-dn.net/?f=56.00)
Standard deviation=![4.0988](https://tex.z-dn.net/?f=4.0988)
c) Mean = ![=24](https://tex.z-dn.net/?f=%3D24)
Standard deviation=![2.4495](https://tex.z-dn.net/?f=2.4495)
Step-by-step explanation:
To compute Mean and standard deviation , we use following formula:
Mean = ![n\pi](https://tex.z-dn.net/?f=n%5Cpi)
Standard deviation=![\sqrt{n\pi(1-\pi)}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%5Cpi%281-%5Cpi%29%7D)
a. ![n=42,\ \pi=0.90](https://tex.z-dn.net/?f=n%3D42%2C%5C%20%5Cpi%3D0.90)
Mean = ![42\times0.90=37.80](https://tex.z-dn.net/?f=42%5Ctimes0.90%3D37.80)
Standard deviation=![\sqrt{42(0.90)(0.10)}=\sqrt{3.78}\approx1.9442](https://tex.z-dn.net/?f=%5Csqrt%7B42%280.90%29%280.10%29%7D%3D%5Csqrt%7B3.78%7D%5Capprox1.9442)
b. ![n=80,\ \pi=0.70](https://tex.z-dn.net/?f=n%3D80%2C%5C%20%5Cpi%3D0.70)
Mean = ![80\times0.70=56.00](https://tex.z-dn.net/?f=80%5Ctimes0.70%3D56.00)
Standard deviation=![\sqrt{80(0.70)(0.30)}=\sqrt{16.8}\approx4.0988](https://tex.z-dn.net/?f=%5Csqrt%7B80%280.70%29%280.30%29%7D%3D%5Csqrt%7B16.8%7D%5Capprox4.0988)
c. ![n=32,\ \pi=0.75](https://tex.z-dn.net/?f=n%3D32%2C%5C%20%5Cpi%3D0.75)
Mean = ![32\times0.75=24](https://tex.z-dn.net/?f=32%5Ctimes0.75%3D24)
Standard deviation=![\sqrt{32(0.75)(0.25)}=\sqrt{6}\approx2.4495](https://tex.z-dn.net/?f=%5Csqrt%7B32%280.75%29%280.25%29%7D%3D%5Csqrt%7B6%7D%5Capprox2.4495)
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Answer:
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Step-by-step explanation:
Formula:
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C = 6.28 x 9 cm
C = 56.52 cm
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Answer:
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Step-by-step explanation
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