Twelve million threehundred and seventy five thousand ans three
Given:
Population proportion,
![\mu _{p}](https://tex.z-dn.net/?f=%5Cmu%20_%7Bp%7D)
= 57% = 0.57
Population standard deviation, σ = 3.5% = 0.035
Sample size, n = 40
Confidence level = 95%
The standard error is
![SE_{p} = \sqrt{ \frac{p(1-p)}{n} } = \sqrt{ \frac{0.57*0.43}{40} } =0.0783](https://tex.z-dn.net/?f=SE_%7Bp%7D%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%20%7D%20%3D%20%5Csqrt%7B%20%5Cfrac%7B0.57%2A0.43%7D%7B40%7D%20%7D%20%3D0.0783)
The confidence interval is
![\hat{p} \pm z^{*}SE_{p}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%20%5Cpm%20z%5E%7B%2A%7DSE_%7Bp%7D)
where
![\hat{p}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D)
= sample proportion
z* = 1.96 at the 95% confidence lvvel
The sample proportion lies in the interval
(0.57-1.96*0.0783, 0.57+1.96*0.0783) = (0.4165, 0.7235)
Answer: Between 0.417 and 72.4), or between (41% and 72%)
Step-by-step explanation:
Distance = rate × time
If b is the speed of the boat in still water, and c is the speed of the current, then:
60 = (b + c) × 4
35 = (b − c) × 3.5
Simplifying:
15 = b + c
10 = b − c
Add the equations together:
25 = 2b
b = 12.5
Plug into either equation to find c:
c = 2.5
The speed of the boat is 12.5 km/h, and the speed of the current is 2.5 km/h.