Answer:
Sample size is ![n=423](https://tex.z-dn.net/?f=n%3D423)
Step-by-step explanation:
Given that,
Margin of error
%
Confidence level
%
Suppose, sample proportion![=0.5](https://tex.z-dn.net/?f=%3D0.5)
i.e. ![\hat{P}=0.5](https://tex.z-dn.net/?f=%5Chat%7BP%7D%3D0.5)
We know that,
Margin of error ![=2^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }](https://tex.z-dn.net/?f=%3D2%5E%2A%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%20%7D)
∴ ![1.64\sqrt{\frac{0.5(0.5)}{n} } \leq 4\%](https://tex.z-dn.net/?f=1.64%5Csqrt%7B%5Cfrac%7B0.5%280.5%29%7D%7Bn%7D%20%7D%20%5Cleq%204%5C%25)
![\Rightarrow 1.64\sqrt{\frac{0.25}{n} } \leq 0.04](https://tex.z-dn.net/?f=%5CRightarrow%201.64%5Csqrt%7B%5Cfrac%7B0.25%7D%7Bn%7D%20%7D%20%5Cleq%200.04)
![\Rightarrow \frac{0.5}{\sqrt{n} } \leq \frac{0.04}{1.64}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B0.5%7D%7B%5Csqrt%7Bn%7D%20%7D%20%5Cleq%20%5Cfrac%7B0.04%7D%7B1.64%7D)
![\Rightarrow \frac{0.5}{\sqrt{n} } \leq 0.0243](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B0.5%7D%7B%5Csqrt%7Bn%7D%20%7D%20%5Cleq%200.0243)
![\Rightarrow \sqrt{n}\geq \frac{0.5}{0.0243}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Csqrt%7Bn%7D%5Cgeq%20%5Cfrac%7B0.5%7D%7B0.0243%7D)
![\Rightarrow \sqrt{n}\geq 20.57](https://tex.z-dn.net/?f=%5CRightarrow%20%5Csqrt%7Bn%7D%5Cgeq%2020.57)
squaring on both side,
∴ ![n=423.1249](https://tex.z-dn.net/?f=n%3D423.1249)
Hence, the sample size is,
![n=423](https://tex.z-dn.net/?f=n%3D423)
Hence, the correct option is ![(b).](https://tex.z-dn.net/?f=%28b%29.)
Answer:
1067
Step-by-step explanation:
Given that:
Error (E) = 0.03
Confidence interval = 95% = 0.95
Sample size (n) = ((Zα/2) / Error)^2 * p(1 - p)
Since no assumption is given ; p = 0.5
α = 0.95
Z(1-α/2) = 1.96
(1.96 / 0.03)^2 * 0.5(1 - 0.5)
(65.333333)^2 * 0.5(0.5)
4268.4444 * 0.25
= 1067.1111
n = 1067
Answer:
$430
Step-by-step explanation:
According to current overtime pay laws, every hour worked over 40 weekly hours must be paid at a rate of 1.5 times the regular hourly rate. Jason Gomi has worked 2 hours of overtime, his gross wages for the week are:
![W = 40*\$10+(2*1.5*\$10)\\W=\$430](https://tex.z-dn.net/?f=W%20%3D%2040%2A%5C%2410%2B%282%2A1.5%2A%5C%2410%29%5C%5CW%3D%5C%24430)
Jason's gross wages for the week are $430.
Answer:
B. 195.5 kg
Step-by-step explanation:
Given
Weight in pounds = 430 pounds
1 kilogram = 2.2 pounds
Required
The weight in kilogram
Let x represents the weight of the humpback's whale's heart in kilogram
Such that;
By Cross multiplication
![x * 2.2lb = 430lb * 1kg](https://tex.z-dn.net/?f=x%20%2A%202.2lb%20%3D%20430lb%20%2A%201kg)
Divide both sides by 2.2lb
![\frac{x * 2.2lb}{2.2lb} = \frac{430lb * 1kg}{2.2lb}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%20%2A%202.2lb%7D%7B2.2lb%7D%20%3D%20%5Cfrac%7B430lb%20%2A%201kg%7D%7B2.2lb%7D)
![x = \frac{430lb * 1kg}{2.2lb}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B430lb%20%2A%201kg%7D%7B2.2lb%7D)
![x = \frac{430lb1kg}{2.2lb}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B430lb1kg%7D%7B2.2lb%7D)
![x = \frac{4301kg}{2.2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B4301kg%7D%7B2.2%7D)
![x = 195.454545 kg](https://tex.z-dn.net/?f=x%20%3D%20195.454545%20kg)
Approximate
![x = 195.5kg](https://tex.z-dn.net/?f=x%20%3D%20195.5kg)
Hence, the weight of the heart is 195.5kg