Answer: ![0.939\ or\ 93.9\%](https://tex.z-dn.net/?f=0.939%5C%20or%5C%2093.9%5C%25)
Step-by-step explanation:
Given
Survey shows that 16% of college students have dogs and 38% have HBO subscription
Probability that a random person have both is
![\Rightarrow P_o=0.16\times 0.38\quad [\text{As both events are independent}]\\\Rightarrow P_o=0.0608](https://tex.z-dn.net/?f=%5CRightarrow%20P_o%3D0.16%5Ctimes%200.38%5Cquad%20%5B%5Ctext%7BAs%20both%20events%20are%20independent%7D%5D%5C%5C%5CRightarrow%20P_o%3D0.0608)
The probability that the random person has neither of the two is
![\Rightarrow P=1-P_o\\\Rightarrow P=1-0.0608\\\Rightarrow P=0.939](https://tex.z-dn.net/?f=%5CRightarrow%20P%3D1-P_o%5C%5C%5CRightarrow%20P%3D1-0.0608%5C%5C%5CRightarrow%20P%3D0.939)
Answer:
x ≈ 83.7
Step-by-step explanation:
You are given a right triangle with the hypotenuse, an acute angle, and the side adjacent to the angle marked. The hypotenuse is unknown. The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
Filling in the given information, we have ...
cos(48°) = 56/x
x = 56/cos(48°) . . . . . multiply by x/cos(48°)
x ≈ 83.7
Answer: The margin of error = ![3\%](https://tex.z-dn.net/?f=3%5C%25)
Step-by-step explanation:
Given
Sample size (n) = 1000
Population proportion = 0.4
= 1 - confidence level
= 1 - 0.95
= 0.05
![margin\; of\; error = z_{\frac{\alpha }{2}}\sqrt{\frac{{\widehat{p}}{(1 -\widehat{p})}}{n}}](https://tex.z-dn.net/?f=margin%5C%3B%20%20of%5C%3B%20%20error%20%3D%20z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%7D%5Csqrt%7B%5Cfrac%7B%7B%5Cwidehat%7Bp%7D%7D%7B%281%20-%5Cwidehat%7Bp%7D%29%7D%7D%7Bn%7D%7D)
![margin\; of\; error = z_{\frac{0.05 }{2}\sqrt{\frac{{(0.4)}{(1 -0.4)}}{1000}}](https://tex.z-dn.net/?f=margin%5C%3B%20%20of%5C%3B%20%20error%20%3D%20z_%7B%5Cfrac%7B0.05%20%7D%7B2%7D%5Csqrt%7B%5Cfrac%7B%7B%280.4%29%7D%7B%281%20-0.4%29%7D%7D%7B1000%7D%7D)
![= z_{0.025}\sqrt{\frac{{(0.4)}{(0.6)}}{1000}}](https://tex.z-dn.net/?f=%3D%20z_%7B0.025%7D%5Csqrt%7B%5Cfrac%7B%7B%280.4%29%7D%7B%280.6%29%7D%7D%7B1000%7D%7D)
![= 1.96\sqrt{\frac{{(0.4)}{(0.6)}}{1000}}](https://tex.z-dn.net/?f=%3D%201.96%5Csqrt%7B%5Cfrac%7B%7B%280.4%29%7D%7B%280.6%29%7D%7D%7B1000%7D%7D)
= 0.03
The margin of error change to
to ![3\%](https://tex.z-dn.net/?f=3%5C%25)
20% of 120 is 24 so you subtract 24 from 120 which is 96:)
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