What is the surface area of this shape?

a packe of cards conatins 4 red and 5 black cards. a hand of 5 cards is drawn without replacment. What is the proablity of all f

Vladimir79 [104]

Answer: Our required probability is 0.3387.

Step-by-step explanation:

Since we have given that

Number of red cards = 4

Number of black cards = 5

Number of cards drawn = 5

We need to find the probability of getting exactly three black cards.

Probability of getting a black card = $\dfrac{5}{9}$

Probability of getting a red card = $\dfrac{4}{9}$

So, using "Binomial distribution", let X be the number of black cards:

$P(X=3)=^5C_3(\dfrac{5}{9})^3(\dfrac{4}{9})^2\\\\P(X=3)=0.3387$

Hence, our required probability is 0.3387.

5 0

3 years ago

The Ohio Department of Agriculture tested 203 fuel samples across the state

Rus_ich [418]

Answer:

$\hat p = \frac{14}{105}= 0.133$

And that represent the proportion of failures.

The confidence interval for the mean is given by the following formula:

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

If we replace the values obtained we got:

$0.133 - 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.0475$

$0.133 + 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.2185$

The 99% confidence interval would be given by (0.0475;0.2185)

Step-by-step explanation:

Previous concept

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58$

The proportion estimated would be:

$\hat p = \frac{14}{105}= 0.133$

And that represent the proportion of failures.

The confidence interval for the mean is given by the following formula:

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

If we replace the values obtained we got:

$0.133 - 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.0475$

$0.133 + 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.2185$

The 99% confidence interval would be given by (0.0475;0.2185)

3 0

3 years ago

Read 2 more answers

The total surface area of a cone whose radius is 2 r and slant height 2l is

vampirchik [111]

Answer:

$A=4\pi r(l+r)$

Step-by-step explanation:

The total surface area of a cone is given by :

$A=\pi rl+\pi r^2\\\\=\pi r(l+r)$

Put r = 2r and l = 2l in the above formula

$A=\pi \times 2r(2l+2r)\\\\A=2\pi r(2l+2r)\\\\=2\pi r \times 2(l+r)\\\\=4\pi r(l+r)$

Hence, the total surface area of the cone is $4\pi r(l+r)$ .

7 0

2 years ago

Plz plz plzzzz help plz !!!

bixtya [17]

I think the last two are correct.
Hope it helps

8 0

3 years ago

Let μ denote the true average radioactivity level(picocuries per liter). The value 5 pCi/L is considered thedividing line betwee

VMariaS [17]

Answer:

H0: μ = 5 versus Ha: μ < 5.

Step-by-step explanation:

Given:

μ = true average radioactivity level(picocuries per liter)

5 pCi/L = dividing line between safe and unsafe water

The recommended test here is to test the null hypothesis, H0: μ = 5 against the alternative hypothesis Ha: μ < 5.

A type I error, is an error where the null hypothesis, H0 is rejected when it is true.

We know type I error can be controlled, so safer option which is to test H0: μ = 5 vs Ha: μ < 5 is recommended.

Here, a type I error involves declaring the water is safe when it is not safe. A test which ensures that this error is highly unlikely is desirable because this is a very serious error. We prefer that the most serious error be a type I error because it can be explicitly controlled.

7 0

3 years ago

What is the surface area of this shape?​

What is the surface area of this shape?