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3 years ago

A major metropolitan newspaper selected a simple random sample of 1,600 readers from their list of 100,000 subscribers.

Mathematics

1 answer:

Tpy6a [65]3 years ago

5 0

Answer: $(0.36845,\ 0.43155)$

Step-by-step explanation:

Let p be the population proportion of readers who would like more coverage of local news.

As per given , we have

sample size :=1600

sample proportion : $\hat{p}=40\%=0.40$

The confidence interval for population proportion is given by :-

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

From z-table ,

For 99% confidence interval the z-value is 2.576.

Substitute all the values in the above formula , we get

The 99% confidence interval for the proportion of readers who would like more coverage of local news as

$0.40\pm(2.576) \sqrt{\dfrac{0.40(1-0.40)}{1600}}$

$0.40\pm(2.576) \sqrt{\dfrac{0.24}{1600}}$

$0.40\pm(2.576) \sqrt{0.00015}$

$0.40\pm(2.576) (0.0122474487139)$

$0.40\pm0.03155$

$(0.40-0.03155,\ 0.40+0.03155)=(0.36845,\ 0.43155)$

Hence, the 99% confidence interval for the proportion of readers who would like more coverage of local news is $(0.36845,\ 0.43155)$ .

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Answer:

3808ft²

Step-by-step explanation:

Formula: A=L×W

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A= 112 × 34= 3808ft²

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3 years ago

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hram777 [196]

Answer:

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Step-by-step explanation:

Cheryl = 7 + 5 = £12

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3 years ago

The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x

natulia [17]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

Firstly we will calculate the general probability that of P(a < X < b)

P(a < X < b) = $\int_{a}^{b} \frac{2}{x^{3}} dx$ = $2\int_{a}^{b} x^{-3} dx$

= $2[ \frac{x^{-3+1} }{-3+1}]^{b}_a dx$ { Because $\int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a$ }

= $2[ \frac{x^{-2} }{-2}]^{b}_a$ = $\frac{2}{-2} [ x^{-2} ]^{b}_a$

= $-1 [ b^{-2} - a^{-2} ]$ = $\frac{1}{a^{2} } - \frac{1}{b^{2} }$

a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }

Comparing with general probability we get,

P(1 < X < 5) = $\frac{1}{1^{2} } - \frac{1}{5^{2} }$ = $1 - \frac{1}{25}$ = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/ $8^{2}$ - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = $\frac{1}{6^{2} } - \frac{1}{10^{2} }$ = $\frac{1}{36} - \frac{1}{100 }$ = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

= $(\frac{1}{1^{2} } - \frac{1}{6^{2} })$ + (1/ $10^{2}$ - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

⇒ P(1 < X < x) = 0.75

⇒ $\frac{1}{1^{2} } - \frac{1}{x^{2} }$ = 0.75

⇒ $\frac{1} {x^{2} }$ = 1 - 0.75 = 0.25

⇒ $x^{2}$ = $\frac{1}{0.25}$ ⇒ $x^{2}$ = 4 ⇒ x = $2$

Therefore, value of x such that P(X < x) = 0.75 is 2.

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3 years ago

I now have another question to ask.

marissa [1.9K]

Answer:

23.6 ft

Step-by-step explanation:

Sketch a right triangle representing this situation. The length of the hypotenuse is 26 ft and the angle of elevation from ground to top of ladder is 65°. The "opposite side" is the reach of the ladder, which we'll call x.

Then:

opp

sin 65° = ----------
26 ft

or (26 ft)(sin 65°) = opp side = height off the ground of top of ladder.

Evaluating this, we get:

(26 ft)(0.906) = 23.56 ft, or, rounded off, 23.6 ft

The ladder reaches 23.6 ft up the side of the building.

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3 years ago

You deposit $300 into a savings account that pays 4% interest compounded annually. How much interest will you earn after 5 years

sammy [17]

Answer:

365

Step-by-step explanation:

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3 years ago