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3 years ago

How do you do this problem and what are the conditions met that makes this a binomial distribution(all 3 conditions)?

Mathematics

2 answers:

ExtremeBDS [4]3 years ago

8 0

The three conditions of a binomial distribution are:

Each trial has two outcomes (eg: "yes or no", "true or false", "red chip or not red chip", etc)
There are a fixed number of trials. This is the value of n.
Each trial has the same probability of success. This is the value of p.

In this case, all of the conditions of a binomial have been met because...

There are two outcomes. We either get a red chip, or we don't get a red chip. I'm focusing on the red chips because the question asks about the probability of getting 1 red chip.
We have n = 5 trials, where each trial consists of selecting a chip and putting it back. It's important to put the chip back so that p is not altered.
The probability of success is p = 6/9 = 2/3 This is the probability of selecting a red chip. This is because there are 6 red out of 6+3 = 9 total.

Since we only want one red chip, and there are 5 slots to fill (1 red+4 black), this must mean there are exactly 5 ways to get what we want.

We could have the following selections

RBBBB
BRBBB
BBRBB
BBBRB
BBBBR

With R = red and B = black. This value 5 will be used as the binomial coefficient. You can find this value through the use of the nCr combination formula or using Pascal's Triangle.

Note: we only have 3 black chips, but because we put the chip back each time, it means we can get more than 3 black selections.

We'll also be using x = 1 to find the probability of getting exactly one red chip

P(x) = (binomialCoefficient)*(p)^x*(1-p)^(n-x)

P(x) = 5*(p)^x*(1-p)^(n-x)

P(1) = 5*(2/3)^1*(1-2/3)^(5-1)

P(1) = 0.0411523

The probability of getting exactly one red chip is roughly 0.0411523

faust18 [17]3 years ago

4 0

Answer:

0.04112

Step-by-step explanation:

The total number of chips here are 6 + 3 = 9 chips

The probability of there being red chips would be 6/9 = 2/3rds = 0.67

According to the binomial theorem P(x) = C(n, x) * px * (1 - p)(n - x). We know that the process is repeated until 5 chips have been drawn, so n = 5. The probability that one red chip is selected would make x = 1, so we would have to solve for P(1).....substituting appropriate values;

P(1) = C(5, 1) * 0.67^1 * (1 - 0.67)^4

= 0.67 * 5.1(1 - 0.67)^4C

= 0.33^4 * 0.67 * 5.1C

= 0.33^4 * 3.417C

= (About) 0.04112...C

The probability that one chip was selected would be about 0.04112

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Place value of 7 in 872 164

Olin [163]

Answer:

hundred thousand

Step-by-step explanation:

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3 years ago

Read 2 more answers

If a scale factor of 4.6 is applied to the parallelogram, what will be the perimeter of the new parallelogram?

anyanavicka [17]

Answer:

The new perimeter is 4.6 times the original perimeter of the parallelogram.

Step-by-step explanation:

A parallelogram is a four-sided figure, such that the opposite sides are parallel.

So a parallelogram is defined by two measures, we can define them as the length L and the width W (W can be equal to L, as in the case of the square or the rhombus)

The perimeter of one parallelogram is then:

P = 2*L + 2*W = 2*(L + W)

If a scale factor of 4.6 is applied to the parallelogram, then all the dimensions must be multiplied by 4.6

This means that the new length is L' = 4.6*L and the new width is W' = 4.6*W

Then the new perimeter is:

P' = 2*W' + 2*L' = 2*(L' + W') = 2*(4.6*L + 4.6*W) = 4.6*[2*(L + W)]

And the thing inside brackets is equal to the original perimeter, then:

P' = 4.6*P

The new perimeter is 4.6 times the original perimeter of the parallelogram.

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3 years ago

Suppose we are interested in analyzing the weights of NFL players. We know that on average, NFL players weigh 247 pounds with a

tigry1 [53]

Answer:

$SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58$

$ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073$

$\bar X - ME = 237- 14.073 = 222.927$

$\bar X + ME = 237+ 14.073 = 251.073$

$n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238$

So the answer for this case would be n=238 rounded up to the nearest integer

Null hypothesis: $\mu \geq 247$

Alternative hypothesis: $\mu$

$z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165$

$p_v =P(z$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is lower than 247 at 10% of significance.

Step-by-step explanation:

For this case we have the following data given:

$\bar X =237$ represent the sample mean

$\sigma = 47$ represent the population deviation

$n =30$ represent the sample size selected

$\mu_0 = 247$ represent the value that we want to test.

The standard error for this case is given by:

$SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58$

For the 90% confidence the value of the significance is given by $\alpha=1-0.9 = 0.1$ and $\alpha/2 = 0.05$ so we can find in the normal standard distribution a quantile that accumulates 0.05 of the area on each tail and we got:

$z_{\alpha/2}= 1.64$

And the margin of error would be:

$ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073$

The confidence interval for this case would be given by:

$\bar X - ME = 237- 14.073 = 222.927$

$\bar X + ME = 237+ 14.073 = 251.073$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

Replacing into formula (b) we got:

$n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238$

So the answer for this case would be n=238 rounded up to the nearest integer

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is lower than 247 pounds, the system of hypothesis would be:

Null hypothesis: $\mu \geq 247$

Alternative hypothesis: $\mu$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165$

P-value

Since is a left tailed test the p value would be:

$p_v =P(z$

Conclusion

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3 years ago

The price dark roasted coffee beans is $11 per pound.

Mademuasel [1]

If the change in the number of pounds is p, the change in the cost will be $11c.
This is because each pound costs $11.

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4 years ago

The product of two numbers is 342. If one number is 18, what is the other nnumber without the use of a calculator show all your

dalvyx [7]

342/18 18 x 10= 180 342 - 180= 162 18 x 9= 90 + 72= 162 10+9= 19 The answer is 19

7 0

3 years ago