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V125BC [204]
3 years ago
13

When 258 college students are randomly selected and surveyed, it is found that 106 own a car. Find a 99% confidence interval for

the true proportion of all college students who own a car. 0.351 < p < 0.471 0.332 < p < 0.490 0.339 < p < 0.482 0.360 < p < 0.461
Mathematics
1 answer:
juin [17]3 years ago
3 0

Answer: 0.332 < p < 0.490

Step-by-step explanation:

We know that the confidence interval for population proportion is given by :-

\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

, where n= sample size

\hat{p} = sample proportion

z* = critical z-value.

As per given , we have

n= 258

Sample proportion of college students who own a car = \hat{p}=\dfrac{106}{258}\approx0.411

Critical z-value for 99% confidence interval is 2.576. (By z-table)

Therefore , the  99% confidence interval for the true proportion(p) of all college students who own a car will be :0.411\pm (2.576)\sqrt{\dfrac{0.411(1-0.411)}{258}}\\\\=0.411\pm (2.576)\sqrt{0.00093829}\\\\= 0.411\pm (2.576)(0.0306315197142)\\\\=0.411\pm 0.0789=(0.411-0.0789,\ 0.411+0.0789)\\\\=(0.3321,\ 0.4899)\approx(0.332,\ 0.490)

Hence, a 99% confidence interval for the true proportion of all college students who own a car : 0.332 < p < 0.490

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Answer:

4\frac{3}{4} or 4.75

Step-by-step explanation:

first we're going to convert the number into improper fractions.

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For subtracting it is suitable to adjust both fractions to an equal denominator, so we're going to multiply \frac{15}{2}x2, it'll equal the same number.

So now we have \frac{30}{4}-\frac{11}{4}, 30-11= 19.

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As you can see I also added 4.75 as an answer, that's if the answer must be a decimal.

I hope this helps you!

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What is an equation of the line that passes through the point (2,−6) and is parallel to the line x-2y=8
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Answer:

y=\frac{1}{2}x-7, or x-2y=14

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the point (2, -6) and is parallel to the line x-2y=8

First, we need to find the slope of x-2y=8, since parallel lines have the same slopes

We can convert the equation from standard form (ax+by=c) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept), in order to help us find the slope of the line

Start by subtracting x from both sides

-2y=-x+8

Divide both sides by -2

y=\frac{1}{2}x-4

The slope of the line x-2y=8 is 1/2

It's also the slope of the line parallel to it.

Since we know the slope of the line, we can plug it into the equation for slope intercept form:

y=\frac{1}{2}x+b

Now we need to find b.

As the equation of the line passes through (2, -6), we can use it to help solve for b

Substitute -6 as y and 2 as x:

-6=\frac{1}{2}(2)+b

Multiply

-6=1+b

Subtract 1 from both sides

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Substitute -7 as b into the equation:

y=\frac{1}{2}x-7

The equation can be left as that, or you can convert it into standard form if you wish.

In that case, you will need to move 1/2x to the other side:

-\frac{1}{2}x+y=-7

A rule about the coefficients a, b, and c in standard form is that a (coefficient in front of x) CANNOT be negative, and every coefficient must be an integer (a whole number, not a fraction or decimal).

So multiply both sides by -2 in order to clear the fraction, as well as change the sign of a

x-2y=14

Hope this helps!

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3 years ago
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