Consider the following dice game, as played at a certain gambling casino: players 1 and 2 roll a pair of dice in turn. the bank then rolls the dice to determine the outcome according to the following rule: player i,i=1,2, wins if his roll is strictly


Ii={1 if i wins, 0 otherwise}


and show that I1 and I2 are positively correlated. Explain why this result was to be expected.

Answer:

Step-by-step explanation:

Random sampling is a procedure for sampling from a population in which (a) the selection of a sample unit is based on chance and (b) every element of the population has a known, non-zero probability of being selected.

Answer:

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.

I hope this helped...

Answer:

10

Step-by-step explanation:

First multiply 9 by 2.5

Then divide 225 by 22.5

Answer:

Finding 1/5 of something is the same as dividing that number by 5. Since 24 isn't divisible by 5, 24 / 5 is not an integer. Since you can't have 4.8 species of animals the answer to (a) is no.

For (b), 1/3 * 24 = 8 and 24 - 8 = 16.

Answer:

€113.67

Step-by-step explanation:

£3 = €4

£85.40 is €x

Cross multiply.

[tex]4 \times 85.4=3x[/tex]

[tex]3x=341.6[/tex]

[tex]\frac{3x}{3}=\frac{341.6}{3}[/tex]

[tex]x=113.86666...[/tex]

The answer is B..........

Answer:

B. 1

Step-by-step explanation:

If it was more than one it wouldn't be a triangle.

Answer: Biased sample

Step-by-step explanation:

This is a biased sample because only students with strong opinions are likely going to volunteer or show interest in representing the school at the board meeting. This sample is a voluntary type sample, and at such the conclusion is not valid. This sample is biased because a group or population of students have a higher or lower sampling probability.

Answer:

the answer is 6!!!!!!

Step-by-step explanation:

The missing value in the table is 5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

An intravenous fluid is infused at the rate shown in the table

Minutes         Milliliters

3                            4

?                             12

2.                            3

?                             6

3                             9

9                             24

Slope=24-9/9-3

=15/3

=5

Now 5=12-4/x-3

5=8/x-3

5x-15=8

5x=23

x=23/5

x=4.6

x=5

The missing number is 5.

Hence, the missing value in the table is 5

To learn more on slope of line click:

https://brainly.com/question/14511992

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Answer:

Answers below

Step-by-step explanation:

a. Is x​ (approximately) a binomial random​ variable?

b. Give the probability distribution for x as a formula.

c. Find p(x = 2).

d. Find P(x <= 1).

Answer:

[tex]x=-10[/tex]

Step-by-step explanation:

[tex]\frac{x}{2}=-5\\\mathrm{Multiply\:both\:sides\:by\:}2\\\frac{2x}{2}=2\left(-5\right)\\Simplify\\x=-10[/tex]

Answer:

We conclude that the mean age of Canadian businesswomen has increased.

Step-by-step explanation:

We are given that according to a report released by CIBC entitled "Women Entrepreneurs: Leading the Charge," the average age for Canadian businesswomen in 2008 was 41.

The researchers randomly sample 97 Canadian businesswomen and ascertain that the sample mean age is 43.4. From past experience, it is known that the population standard deviation is 8.95.

Let [tex]\mu[/tex] = mean age of Canadian businesswomen.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 41      {means that the mean age of Canadian businesswomen has decreased or remained same}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 41     {means that the mean age of Canadian businesswomen has increased}

The test statistics that would be used here One-sample z-test statistics because we know about population standard deviation;

                               T.S. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean age of Canadian businesswomen = 43.4

             [tex]\sigma[/tex] = population standard deviation = 8.95

             n = sample of Canadian businesswomen = 97

So, the test statistics  =  [tex]\frac{43.4-41}{\frac{8.95}{\sqrt{97} } }[/tex]

                                     =  2.64

The value of z test statistic is 2.64.

Also, P-value of the test statistics is given by;

             P-value = P(Z > 2.64) = 1 - P(Z < 2.64)

                           = 1 - 0.99585 = 0.00415

Now, at 1% significance level the z table gives critical value of 2.33 for right-tailed test.

Since our test statistic is more than the critical value of z as 2.64 > 2.33, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean age of Canadian businesswomen has increased.

Answer: 368 ways

Step-by-step explanation: To find the total number of probabilities, you multiply all the factors together to get total outcome. 16 * 23 = 368

Answer: 4/3

Step-by-step explanation:

As you know this graph is a lemniscate

[tex]4\int\limits^1_0 {x\sqrt{1-x^{2} } \, dx =\frac{4}{3} =1.33$[/tex]

Answer:

30

Step-by-step explanation:

It is an equalateral triangle

Here is the full question:

When a species has several variants of a phenotype passed on from generation to generation, we can form a hypothesis about the genetics of the trait based on Mendelian theories of genetic inheritance. For example, in a two-gene dominant epistatic model, the first gene masks the effect of the second gene, leading to the expression of three phenotype variants. Crossing the dominant and recessive homozygote lines would result in a second generation represented by a mix of dominant, intermediate, and recessive phenotype variants in the expected proportions: and respectively, also called a 12:3: 1 ratio.

Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2: 131 white squash, 34 yellow squash, and 10 green squash. Are these data consistent with a 12: 3: 1 dominant epistatic model of genetic inheritance( white being dominant)?

The null hypothesis for the chi-square goodness-of-fit test is                

Answer:

The null  hypothesis for the chi-square goodness-of-fit test is :

[tex]\mathbf{H_o:p_{white} = \frac{12}{16}, p_{yellow} = \frac{3}{16}; p_{green} = \frac{1}{16} }[/tex]

Step-by-step explanation:

The objective of this question is to state the null hypothesis for the  chi-square goodness-of-fit test.

Given that:

There are three colors associated with this model . i,e White , yellow and green and they are in the ratio of 12:3:1

The total number of these color traits associated with this model = 12 + 3 + 1 = 16

Thus ;

The null  hypothesis for the chi-square goodness-of-fit test is :

[tex]\mathbf{H_o:p_{white} = \frac{12}{16}, p_{yellow} = \frac{3}{16}; p_{green} = \frac{1}{16} }[/tex]

Answer:

step 3 is wrong

Step-by-step explanation:

i know it because i did the unit test review

Answer:

D

ヾ(•ω•`)o

Step-by-step explanation:

Answer:

[tex] ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]

The confidence level is 0.98 and the significance is [tex]\alpha=1-0.98 =0.02[/tex] and [tex]\alpha/2 =0.01[/tex] and the critical value using the table is:

[tex]z_{\alpha/2}= 2.326[/tex]

And replacing we got:

[tex] ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex]\sigma = 425[/tex] represent the population deviation

[tex] n =22[/tex] the sample size

[tex]\bar X =1520[/tex] represent the sample mean

We want to find the margin of error for the confidence interval for the population mean and we know that is given by:

[tex] ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]

The confidence level is 0.98 and the significance is [tex]\alpha=1-0.98 =0.02[/tex] and [tex]\alpha/2 =0.01[/tex] and the critical value using the table is:

[tex]z_{\alpha/2}= 2.326[/tex]

And replacing we got:

[tex] ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76[/tex]

Answer:

14, 32

Step-by-step explanation:

45,15,44,17,40,20,31,25

this is combination of 2 series:

In the first series we can see the pattern as:

In the second series we can see the pattern as:

The series will continue as:

Answer:

middle is 2.5 ft

right is 4375 ft

left is 1875 ft

Step-by-step explanation:

Answer:

[tex]n=(\frac{1.960(80)}{25})^2 =246.73 \approx 247[/tex]

So the answer for this case would be n=247 rounded up to the nearest integer

Step-by-step explanation:

We know that the standard deviation is :

[tex]\sigma = 80[/tex] represent the deviation

The margin of error is given by this formula:

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

And on this case we have that ME =25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

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

The critical value for 95% of confidence interval now can be founded using the normal distribution and the critical value would be [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.960(80)}{25})^2 =246.73 \approx 247[/tex]

So the answer for this case would be n=247 rounded up to the nearest integer

Answer:

y-1 = 3(x-2)

Step-by-step explanation:

The point slope form of a line is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y-1 = 3(x-2)

Answer:

Step-by-step explanation:

From the question; we are given the following inclusive frequency distribution information

Class                Frequency f

1.1-1.5                           18

1.6-2.0                         27

2.1-2.5                         31

2.6-3.0                        40

3.1-3.5                         56

3.6-4.0                        55

4.1-4.5                          23

Convert the above inclusive frequency distribution to exclusive frequency distribution with respect of the upper and lower class limit ; we have:

Class                             Frequency f

1.05 - 1.55                             18

1.55 - 2.05                           27

2.05 - 2.55                          31

2.55 - 3.05                          40

3.05 - 3.55                          56

3.55 - 4.05                          55

4.05 - 4.55                          23

Class                             Frequency f                     cf

1.05 - 1.55                             18                              18            

1.55 - 2.05                           27                               45

2.05 - 2.55                          31                               76

2.55 - 3.05                          40                               116

3.05 - 3.55                          56                               172

3.55 - 4.05                          55                               227

4.05 - 4.55                          23                               250

                                       n = 250

To determine the daily sales; we can derive that from estimated Mode by using the relation :

Estimated Mode = L + fm − fm-1(fm − fm-1) + (fm − fm+1) × w

here:

L  = the lower class boundary of the modal group

fm-1 =  the frequency of the group before the modal group

fm = the frequency of the modal group

fm+1 = the frequency of the group after the modal group

w  = the group width

However;

It is easier now to determine  the modal group (i.e the group with the highest frequency), which is 3.05 -3.55

L = 3.05

fm-1 =40

fm =56

fm+1 = 55

w = 0.5

∴[tex]mode = 3.05 + \dfrac{56 - 40 }{(56 - 40) + (56 -55)} * 0.5 \\ \\ mode = 3.05 + 0.4705 \\ \\ mode = 3.5205[/tex]

To find Median Class ; we use the formula;

Median Class = value of (n / 2)th observation

Median Class  = value of (250 / 2)th observation  

Median Class = value of 125th observation

From the column of cumulative frequency cf,

we will see that the 125th observation lies in the class 3.05-3.55.

∴ The median class is 3.05-3.55.

Thus;,  

L=lower boundary point of median class =3.05

n=Total frequency =250

cf=Cumulative frequency of the class preceding the median class =116

f=Frequency of the median class =56

c=class length of median class =0.5

[tex]Median M=L+n2-cff- c \\ \\ =3.05+125-11656⋅0.5 \\ \\=3.05+0.08036 \\ \\ =3.13036[/tex]

hence median sales = $3130.36

Answer:

2 liters of paint.

Step-by-step explanation:

First we nned to know to total area of the wall by using the formula A = lw

A = 4*5 = 20m²

then we given 1 liter cover 10 m², 20 m² = 2 liters of paint.

Answer:

2) Strong Negative Correlation

Step-by-step explanation:

With the value of r we have both the information about the sign of the relationship and the strength of this relationship.

As the value of r is negative, we can conclude that the correlation between x and y is negative.

Also, as the absolute value of r is close to 1, we can conclude that this relationship is strong.

The strength can also be seen in the value of r2, which is also close to 1, but this value does not give information about the sign.

The value of the slope a, being negative, can also tell us that the relation between x and y is a negative correlation.

Answer:

b) -4/3

Step-by-step explanation:

perpendicular lines have slopes that are opposite reciprocals. the opposite of 3/4 is -3/4, and the reciprocal of -3/4 is -4/3. hope this helps!

Answer:

It is -4/3

Step-by-step explanation:

Answer:

Equilateral, acute

Step-by-step explanation:

Equilateral triangles have all sides the same length (all sides are 4 ft in this triangle, so it is equilateral).

Acute triangles have no angles that are greater than or equal to 90 degrees (all angles are 60, which is less than 90, so it is acute).

Answer:

The company will expect to replace 13.03% of batteries.

The company should guarantee the batteries for 35 months.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 45, \sigma = 8[/tex]

If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?

This is the pvalue of Z when X = 36. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{36 - 45}{8}[/tex]

[tex]Z = -1.125[/tex]

[tex]Z = -1.125[/tex] has a pvalue of 0.1303.

The company will expect to replace 13.03% of batteries.

If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries

They should guarantee to the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.28 = \frac{X - 45}{8}[/tex]

[tex]X - 45 = -1.28*8[/tex]

[tex]X = 34.76[/tex]

Rounding to the nearest month

The company should guarantee the batteries for 35 months.

Answer:

c of what im sure about

Step-by-step explanation:

The value of X is 4

please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Answer:

[tex]31400\mu m^2[/tex]

Step-by-step explanation:

We are given that

Diameter of egg,d=[tex]100\mu m[/tex]

We have to find the  surface area of egg in [tex]\mu m^2[/tex].

Radius of egg,r=[tex]\frac{d}{2}=\frac{100}{2}=50\mu m[/tex]

Surface area of sphere=[tex]4\pi r^2[/tex]

Where [tex]\pi=3.14[/tex]

Using the formula

Surface area of egg=[tex]4\times 3.14(50)^2[/tex]

Surface area of egg=[tex]31400\mu m^2[/tex]

Hence, the surface area of the egg=[tex]31400\mu m^2[/tex]

Answer:

10x-15a

Step-by-step explanation: