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1 year ago

You toss a fair coin 10000 times. what are the odds of obtaining more than 5100 tails, approximately?

1 answer:

3 0

This can be solved by using the normal approximation to the binomial distribution.
mean = np = 10.000 * 0.5 = 5,000
The standard deviation is given by:
$S.D.= \sqrt{npq} = \sqrt{5000\times0.5} =50$
$z=\frac{5100-5000}{50}=2$
The probability of obtaining more than 5100 tails is 0.0228 and the probability of obtaining fewer than 5100 tails is 0.9772.
The odds of obtaining more than 5100 tails is therefore:
0.0228:0.9772 = 1:42.86.

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Of the 500 sample households in the previous exercise, 7 had three or more large-screen TVs. (a) The percentage of households in

likoan [24]

Answer:

a) The percentage of households in the town with three or more largescreen TVs is estimated as :

The best estimation for the population proportion is :

$\hat p=\frac{7}{500}=0.014$

And that represent the 1.4%.

b) And the 95% confidence interval would be given (0.00370;0.0243).

And the % would be between 0.37% and 2.43%.

Step-by-step explanation:

Data given and notation

n=500 represent the random sample taken

X=7 represent the households with three or more large-screen TVs

$\hat p=\frac{7}{500}=0.014$ estimated proportion of households with three or more large-screen TVs

$\alpha=0.05$ represent the significance level (no given, but is assumed)

z would represent the statistic (variable of interest)

p= population proportion of households with three or more large-screen TVs

Part a

The percentage of households in the town with three or more largescreen TVs is estimated as :

The best estimation for the population proportion is :

$\hat p=\frac{7}{500}=0.014$

And that represent the 1.4%.

Part b

Yes is possible. We hav that $np>10$ and $n(1-p)>10$ so we have the assumption of normality to find the interval.

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.014 - 1.96 \sqrt{\frac{0.014(1-0.014)}{500}}=0.00370$

$0.014 + 1.96 \sqrt{\frac{0.014(1-0.014)}{500}}=0.0243$

And the 95% confidence interval would be given (0.00370;0.0243).

And the % would be between 0.37% and 2.43%.

4 0

2 years ago

Kx + 3x = 4 solve for x.

victus00 [196]

Take out a common factor between 3x and kx. That means use the distributive law to get what you normally would start with.

x(k + 3) = 4

Now divide by k + 3

x = 4/(k + 3)

That's as much as you can do with this question.

4 0

1 year ago

Use Euler's formula to derive the identity. (Note that if a, b, c, d are real numbers, a + bi = c + di means that a = c and b =

storchak [24]

Answer with Step-by-step explanation:

We have to prove that

$sin 2\theta=2sin\theta cos\theta$ by using Euler's formula

Euler's formula : $e^{i\theta}=cos\theta+isin\theta$

$e^{i(2\theta)}=(e^{i\theta})^2$

By using Euler's identity, we get

$cos2\theta+isin2\theta=(cos\theta+isin\theta)^2$

$cos2\theta+isin2\theta=(cos^2\theta-sin^2\theta+2isin\theta cos\theta)$

$(a+b)^2=a^2+b^2+2ab, i^2=-1$

$cos2\theta+isin2\theta=cos2\theta+i(2sin\theta cos\theta)$

$cos2\theta=cos^2\theta-sin^2\theta$

Comparing imaginary part on both sides

Then, we get

$sin2\theta=2sin\theta cos\theta$

Hence, proved.

8 0

2 years ago

Alice purchased 4 1⁄2 kilograms of olive oil for $27. What is the price per kilogram?

vitfil [10]

Hi!

We will solve this using ratios, like this:

4 1/2 = 4,5 kg of olive oil for 27 $

1 kg of olive oil for x $

_____________________________

x = (27*1)/4,5

x = 27/4,5

x = 6 $ per kilogram

Hope this helps!

8 0

2 years ago

Two sides of a triangle have lengths 12 m and 14 m. The angle between them is increasing at a rate of 2°/min. How fast is the le

Dvinal [7]

Answer:

1.692 m/min

Step-by-step explanation:

Let $\theta$ be the angle between the two sides and x be the length of the third side. By cosine rule,

$x^2 = 12^2+14^2-2\times12\times14\cos\theta = 340 - 336\cos\theta$

$x= \sqrt{340 - 336\cos\theta}$

We differentiate x with respect to $\theta$ by applying chain rule.

$\dfrac{dx}{d\theta} = \dfrac{336\sin\theta}{2\sqrt{340 - 336\cos\theta}} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}}$

Rate of change of $\theta$ is 2

$\dfrac{\theta}{dt} = 2$

Rate of change of x is

$\dfrac{dx}{dt} = \dfrac{dx}{d\theta}\times\dfrac{d\theta}{dt}$

$\dfrac{dx}{dt} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}} \times2=\dfrac{336\sin\theta}{\sqrt{340 - 336\cos\theta}}$

At 60°,

$\dfrac{dx}{dt} = \dfrac{336\sin60}{\sqrt{340 - 336\cos60}} = 1.692 \text{ m/min}$

4 0

1 year ago