Mathematics, 16.01.2021 16:40 dustinchang49

A die is rolled 25 times and 12 evens are observed. Calculate and interpret a 95% confidence interval to estimate the true proportion of evens rolled on a die.

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The 95% confidence interval to estimate the true proportion of evens rolled on a die is (0.2842, 0.6758). This means that we are 95% sure that for the entire population of dies, the true proportion of evens rolled on a die is between 0.2842 and 0.6758

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 level of $1-\alpha$ , 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 $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 25, \pi = \frac{12}{25} = 0.48$

95% confidence level

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 .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.48 - 1.96\sqrt{\frac{0.48*0.52}{25}} = 0.2842$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.48 + 1.96\sqrt{\frac{0.48*0.52}{25}} = 0.6758$

Answer from: Quest

2x^2 -2x -12 = 02(x -3)(x +2) = 0see below for explanation

step-by-step explanation:

equation

you are asked to write the equation

expression = 0

using the given expression. when you do that, you have

2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

(x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

-6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

x - 3 = 0

x = 3 . . . add 3 to both sides of the equation

x +2 = 0

x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

Answer from: Quest

step-by-step explanation:

goog be able to you with that maybe

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