what is a random variable

Answer:

87.49% probability that the sample average was less than 375 days

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 359, \sigma = 90.4, n = 42, s = \frac{90.4}{\sqrt{42}} = 13.95[/tex]

What is the probability that the sample average was less than 375 days?

This is the pvalue of Z when X = 375. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{375 - 359}{13.95}[/tex]

[tex]Z = 1.15[/tex]

[tex]Z = 1.15[/tex] has a pvalue of 0.8749.

87.49% probability that the sample average was less than 375 days

Answer:

B.

Step-by-step explanation:

Volume of the model of moon = 4/3(πr³)

= 4/3(π)(1)³

= 4.2 feet³

Volume of cylinder = πr²h

= (3.14)(0.5)²(0.5)

= 0.39 feet³

Cylindrical clay boxes to be used = 4.2/0.39

=10.7 ≈ 11

Answer:

We conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.

Step-by-step explanation:

We are given that in a certain school district, it was observed that 24% of the students in the element schools were classified as only children

However, in the special program for talented and gifted children, 119 out of 415 students are only children.

Let p = proportion of only children in the special program.

So, Null Hypothesis, [tex]H_0[/tex] : p = 24%      {means that the proportion of only children in the special program is equal to the proportion for the school district}

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 24%     {means that the proportion of only children in the special program is significantly different from the proportion for the school district}

The test statistics that would be used here One-sample z-test for proportions;

                                T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of only children in the special program = [tex]\frac{119}{415}[/tex] = 0.29

           n = sample of students = 415

The hypothesized population proportion for this test is 0.24.

So, the test statistics  =  [tex]\frac{0.29-0.24}{\sqrt{\frac{0.24(1-0.24)}{415} } }[/tex]  

                                     =  2.385

The value of z test statistic is 2.385.

Now, at 0.05 significance level the z table gives critical value of -1.96 and 1.96 for two-tailed test.

Since our test statistic doesn't lie within the range of critical values of z, 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 proportion of only children in the special program is significantly different from the proportion for the school district.

Answer:

The equation is y=1/2x+5

Step-by-step explanation:

Answer:

y=1/2x+5

Step-by-step explanation:

I learned this last year. I know this is the answer

Answer:

This is the answer EDGE 2020

Answer:

a. 23.02 %

b. 49%

c. W

Step-by-step explanation:

Solution:-

- A multi-variable function for the percentage of fish in the lake that are intolerant to the pollution is given as:

                     [tex]P ( W , R , A ) = 49 - 1.61W - 1.41R - 1.38A[/tex]

Where,

             W: percentage of wetland

             R: percentage of residential area

             A: percentage of agriculture

- We are to evaluate the percentage of fish intolerant to pollution in the case where W = 3 , R = 15 , A = 0. We will plug in the values in the modeled function P ( W , R , A ) as follows:

                     [tex]P ( 3 , 15 , 0 ) = 49 - 1.61*3 - 1.41*15 -1.38*0\\\\P ( 3 , 15 , 0 ) = 23.02\\[/tex]

- To determine the maximum percentage of fish that will be intolerant to pollution we will employ the use of critical points. The critical point that is defined by the linear relationship between P and all other parameters ( W, R , A ). The maximum value occurs when W = R = A = 0.

                   [tex]P ( 0 , 0 , 0 ) = 49 - 1.61*0 -1.41*0 - 1.38*0 = 49[/tex]

- Hence, the maximum value of the function is 49%.

- The linear relationship between each induvidual parameter ( R, W , A ) and the function ( P ) is proportional in influence. The extent of influence can be quantized by the constant multiplied by each parameter.

- We see that that ( 1.61*W ) > ( 1.41R ) > ( 1.38A ). The greatest influence is by parameter ( W ) i.e the influence of percentage of wetlands .

Answer:The transformation is described as a rotation of 180 degrees clockwise around the origin.

Step-by-step explanation:

Answer: choice A

Step-by-step explanation:

The shaded area represents the complement of B.

Bc or B’ is the complement of B and B’=1-B or B’=S-B

The probability that Events A and B occur is the probability of the intersection of A and B. The probability of the intersection of Events A and B is denoted by P(A ∩ B), which in this example would be equal to B.

The probability that Events A or B occur is the probability of the union of A and B. The probability of the union of Events A and B is denoted by P(A ∪ B), which in this example is equal to S.

Answer:

27

Step-by-step explanation:

39+4=43

27, 31, 35, 39, 43

Answer:

27

Step-by-step explanation:

When you add u subtract 39 from 43 u will get 4

Therefore u will subtract 4 from 39 to get the third number which is 35 then subtract 4 from it to get the second number which is 31 then subtract another 4 to get the first number that's 27

Answer:

The calculated value t = 2.038< 2.145 at 0.05 level of significance

Null hypothesis is accepted

There is the average rate is less than  μ ≤ 4

Step-by-step explanation:

Step(i):-

The Population of the mean 'μ' =4

sample size   'n' = 16

sample mean 'x⁻' = 4.53

given sample standard deviation 's' = 1.04

level of significance  α = 0.05

Step(ii):-

Null hypothesis:H₀ : There is no significance difference between two means

Alternative hypothesis : H₁: There is significance difference between two means

Test statistic

                    [tex]t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n} } }[/tex]

                   [tex]t = \frac{4.53-4}{\frac{1.04}{\sqrt{16} } }[/tex]

                t = 2.038

Degrees of freedom ν = n-1 = 16-1 =15

t₀.₀₂₅ = 2.145

Conclusion:-

The calculated value t = 2.038< 2.145 at 0.05 level of significance

Null hypothesis is accepted

There is the average rate is less than  μ ≤ 4

Answer:

The largest interval is    [tex]-\infty < 0 < 5[/tex]

Step-by-step explanation:

From the question the equation given is  

       [tex](x-5)y'' + 3y = x \ \ \ y(0) = 0 \ , y'(0) = 1[/tex]  

Now dividing the both sides of this equation by (x-5)

         [tex]y'' + \frac{3y}{(x-5)} = \frac{x}{x-5}[/tex]

Comparing this equation with the standard form of 2nd degree differential which is

        [tex]y'' + P(x)y' + Q(x) y = R(x)[/tex]

We see that

        [tex]Q(x) = \frac{3y}{(x-5)}[/tex]

        [tex]R(x) = \frac{x}{(x-5)}[/tex]

So at x =  5  [tex]Q(x) \ and \ R(x)[/tex] are defined for this equation because from the equation of [tex]Q(x) \ and \ R(x)[/tex]  x =  5 give infinity

This implies that the largest interval which includes x = 0 , P(x) , Q(x) , R(x ) is  

       [tex]-\infty < 0 < 5[/tex]

This because x = 5 is not defined in y domain

Answer:0.92

Step-by-step explanation:

Given

[tex]57\%[/tex] of Population is vaccinated

So, Probability of a person being vaccinated is [tex]P=0.57[/tex]

and simultaneously , probability of not vaccinated is [tex]1-P[/tex]

[tex]=1-0.57=0.43[/tex]

Now, Probability that atleast one of them has been vaccinated is given by

[tex]=1-P(\text{None of them is vaccinated})[/tex]

[tex]=1-0.43\times 0.43\times 0.43[/tex]

[tex]=1-0.0795[/tex]

[tex]=0.92[/tex]

Answer:

The probability that AT LEAST ONE of them has been vaccinated

P( X ≥1)  = 0.920493

Step-by-step explanation:

Step(i):-

Given  57 % of the people have been vaccinated

p = 57% =0.57

q = 1-p =1-0.57 = 0.43

n = 3

[tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]

Step(ii):-

The probability that AT LEAST ONE of them has been vaccinated

P( X ≥1) = P( x =1) + P(x =2)+P(x=3)             [tex]P(X\geq 1) = 3_{C_{1} } (0.57)^{1} (0.43)^{3-1} + 3_{C_{2} } (0.57)^{2} (0.43)^{3-2} + 3_{C_{3} } (0.57)^{3} (0.43)^{3-3}[/tex]

[tex]P(X\geq 1) = 3 (0.57) (0.43)^{2} + 3 (0.57)^{2} (0.43) + 1 (0.57)^{3} (0.43)^{0}[/tex]

               =  0.316179 + 0.419121 +0.185193

            = 0.920493

Final answer:-

The probability that AT LEAST ONE of them has been vaccinated

P( X ≥1)  = 0.920493

Answer:

  see attached for a graph

Step-by-step explanation:

When g(x) is transformed to

  f(x) = f(x -h) +k

The graph of g(x) is translated h units right and k units up.

__

Here, the function g(x) = x^2 is transformed to ...

  f(x) = g(x -3) +12 = (x -3)^2 +12

Then the graph of f(x) is the graph of g(x)=x^2 translated 3 units right and 12 units up.

Answer:

Step-by-step explanation:

here ,

6x +238 = 3x+178 ( vertically opposite angles are equal)

so 6x - 3x = 178 -238

3x =-60

x =-60/3

x=-20

hope it helps / please mark me as the brainliest..

Answer:

x= -20

Step-by-step explanation:

The 2 angles are opposite each other. Therefore, they are vertical angles and congruent. We can set them equal to each other and solve.

6x+238=3x+178

To solve the equation, we want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

First, subtract 3x from both sides

6x-3x+238=3x-3x+178

6x-3x+238=178

3x+238=178

Next, subtract 238 from both sides

3x+238-238=178-238

3x=178-238

3x=-60

Finally, divide both sides by 3.

3x/3= -60/3

x=-60/3

x= -20

Answer:

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Answer:

a) 10.38% probability that the sample mean will be more than 59 pounds.

b) 67.72% probability that the sample mean will be more than 56 pounds.

c) 22.10% probability that the sample mean will be between 56 and 57 pounds.

d) 1.46% probability that the sample mean will be less than 53 pounds.

e) 0% probability that the sample mean will be less than 49 pounds.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 56.8, \sigma = 12.2, n = 49, s = \frac{12.2}{\sqrt{49}} = 1.74285[/tex]

a. More than 59 pounds

This is 1 subtracted by the pvalue of Z when X = 59. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{59 - 56.8}{1.74285}[/tex]

[tex]Z = 1.26[/tex]

[tex]Z = 1.26[/tex] has a pvalue of 0.8962.

1 - 0.8962 = 0.1038

10.38% probability that the sample mean will be more than 59 pounds.

b. More than 56 pounds

This is 1 subtracted by the pvalue of Z when X = 56. So

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

[tex]Z = \frac{56 - 56.8}{1.74285}[/tex]

[tex]Z = -0.46[/tex]

[tex]Z = -0.46[/tex] has a pvalue of 0.3228.

1 - 0.3228 = 0.6772

67.72% probability that the sample mean will be more than 56 pounds.

c. Between 56 and 57 pounds

This is the pvalue of Z when X = 57 subtracted by the pvalue of Z when X = 56. So

X = 57

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

[tex]Z = \frac{57 - 56.8}{1.74285}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a pvalue of 0.5438

X = 56

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

[tex]Z = \frac{56 - 56.8}{1.74285}[/tex]

[tex]Z = -0.46[/tex]

[tex]Z = -0.46[/tex] has a pvalue of 0.3228.

0.5438 - 0.3228 = 0.2210

22.10% probability that the sample mean will be between 56 and 57 pounds.

d. Less than 53 pounds

This is the pvalue of Z when X = 53.

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

[tex]Z = \frac{53 - 56.8}{1.74285}[/tex]

[tex]Z = -2.18[/tex]

[tex]Z = -2.18[/tex] has a pvalue of 0.0146

1.46% probability that the sample mean will be less than 53 pounds.

e. Less than 49 pounds

This is the pvalue of Z when X = 49.

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

[tex]Z = \frac{49 - 56.8}{1.74285}[/tex]

[tex]Z = -4.48[/tex]

[tex]Z = -4.48[/tex] has a pvalue of 0.

0% probability that the sample mean will be less than 49 pounds.

Answer:

1 5/6 gallons

Step-by-step explanation:

1. 5 1/2 = 11/2 gallons

2. She uses: 1/3 x 11/2 = 11/6 gallons

3. so: 11/6 = 1 5/6 gallons

I'M MARIE!!!

78% means 78/100=0.78

Answer:

3 pack of hot dogs and 2 pack of buns 24

Step-by-step explanation:

hot dogs come in packs of 8

burns came in packs of 12

what is the least number of each you can buy in order to have a equal number of hot dogs and buns

so to get equal number

we have to look for the LCM of 8 and 12 = 24

therefore the packs will be equal to product

hot dogs come in packs of 8 = 8*3 = 24

burns came in packs of 12 = 12 *2 = 24

therefore, 3 pack of hot dogs and 2 pack of buns 24

(1) Suppose x = 32.12353535... . Then 100x = 3212.353535... and 10000x = 321235.353535... .

Subtracting these gives

10000x - 100x = 321235.353535... - 3212.353535...

9900x = 321235 - 3212

9900x = 318023

x = 318023/9900

(2) By the same process as above, we start with

x = 2.333...

y = 4.151515...

Then

10x = 23.333...

==>  10x - x = 23.333... - 2.333...

==>  9x = 23 - 2

==>  x = 21/9

and

100y = 415.151515...

==>  100y - y = 415.151515... - 4.151515

==>  99y = 415 - 4

==>  y = 411/99

After this, we get

x + y = 2.333... + 4.151515...

==>  x + y = 21/9 + 411/99

==>  x + y = 231/99 + 411/99

==>  x + y = 642/99 = 214/33

Answer:

V=3

Step-by-step explanation:

2(v-1)+8=6(2v-4)

2V-2+8=12v-24(calculate)

2v+6=12v-24(move terms)

2v-12v=-24-6(collect like terms)

-10v=-30(devide both sides by-10)

V=3

hi I hope this helps.

Answer:

[tex]y = \frac{1}{2} x+1[/tex]

Step-by-step explanation:

Perpendicular => So, it will have a slope of a negative reciprocal to this slope

Slope = m = 1/2

Now,

Point = (x,y) = (0,1)

So, x = 0 and y = 1

Putting this in slope-intercept equation to get b

=> [tex]y = mx+b[/tex]

=> 1 = (1/2)(0) + b

=> b = 1

Now putting m and b in the slope intercept equation to get the required equation

=> [tex]y = \frac{1}{2} x+1[/tex]

Answer:

y = \frac{1}{2} x+1

Step-by-step explanation:

Answer:

Area of the rectangle = 1056 square units

Step-by-step explanation:

Rectangle published could be dissected into nine different squares with different sizes.

Area of the squares with different measure of sides will be,

For side length = 1 unit

Area of the square = (Side)²

= 1²

= 1 square units

For side length = 4 units

Area of the square = 4² = 16 units²

For side length = 7 units

Area of the square = 7² = 49 units²

For side length = 8 units

Area of the square = 8² = 64 units²

For side length = 9 units

Area of the square = 9² = 81 square units

For side length = 10 units

Area of the square = 10² = 100 square units

For side length = 14 units

Area of the square = 14² = 196 square units

For side length = 15 units

Area of the square = 15² = 225 square units

For side length = 18 units

Area of the square = 18² = 324 square units

Total area of the rectangle by adding these 9 squares

= 1 + 16 + 49 + 64 + 81 + 100 + 196 + 225 + 324

= 1056 square units

Answer: D) 180 Minutes

Step-by-step explanation:

If every hour is equal to 60 minutes and the movie (Lord of the Rings) was 3 hours longs...then we just have to multiply....

60 x 3 = 180

I hope this helps!

Answer: itz 780

Step-by-step explanation:

Answer:

The slope of the line is -7/8

When the point (7, –4) is used, the point-slope form of the line is

y+4=(-7/8)(x-7)

The slope-intercept form of the line is y=(-7/8)x+(17/8)

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

a10=a1+(n-1)d

15=-3+(10-1)d

15+3=9d

d=2