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Mathematics

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morpeh [17]3 years ago

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We are studying the proportion of cities that have private garbage collector. We want a maximum error of 0.10 and a 95% confiden

True [87]

Answer:

The minimum number of cities we need to contact is 96.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence interval

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

In this problem, we have that:

$p = 0.5, M = 0.1$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.1 = 1.96*\sqrt{\frac{0.5*0.5}{n}}$

$0.1\sqrt{n} = 0.98$

$\sqrt{n} = 9.8$

$(\sqrt{n})^{2} = (9.8)^{2}$

$n = 96$

The minimum number of cities we need to contact is 96.

8 0

3 years ago

Suppose you have the following recursion formula a1 = 1, a2 = 2, and an = a(n - 1)+ a(n - 2) for integers n ≥ 3. How would you d

Firlakuza [10]

$\left\{\begin{array}{ccc}a_1=1\\a_2=2\\a_n=a_{n-1}+a_{n-2}&for\ n\geq3\end{array}\right\\\\a_3=a_{3-1}+a_{3-2}=a_2+a_1\to a_3=2+1=3\\\\a_4=a_{4-1}+a_{4-2}=a_3+a_2\to a_4=3+2=5\\\\a_5=a_{5-1}+a_{5-2}=a_4+a_3\to a_5=5+3=8\\\vdots$