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A fair die is rolled 8 times. What is the probability that the die comes up 6 exactly twice? What is the probability that the die comes up an odd number exactly five times? Find the mean number of times a 6 comes up. Find the mean number of times an odd number comes up. Find the standard deviation of the number of times a 6 comes up. Find the standard deviation of the number of times an odd number comes up.

Answers

Answer 1

Answer:

Answer:

0.2605, 0.2188, 1.33, 4, 1.0540, 1.4142

Step-by-step explanation:

A fair die is rolled 8 times.

a. What is the probability that the die comes up 6 exactly twice?

b. What is the probability that the die comes up an odd number exactly five times?

c. Find the mean number of times a 6 comes up.

d. Find the mean number of times an odd number comes up.

e. Find the standard deviation of the number of times a 6 comes up.

f. Find the standard deviation of the number of times an odd number comes up.

a. A die is rolled 8 times. If A represent the number of times a 6 comes up. For a fair die the probability that the die comes up 6 is 1/6 - Thus A ~ Bin(8, 1/6)

The probability mass function of the random variable A is

$p(A) = \left \{ {(8!)/(x!(8 - x)!)*((1)/(6) )^(A)*((5)/(6) )^(8-A) } \right. for A=0,1, ...8$

hence, p(6 twice) implies P(A=2)

that is P(2) substitute A = 2

$p(2) = \left \{ {(8!)/(2!(8 - 2)!)*((1)/(6) )^(2)*((5)/(6) )^(8-2) } \right. for A=0,1, ...8$

$p(2)=(8!)/(2!6!) *((1)/(6) )^(2) *((5)/(6) )^(6)$

p(2) = 0.2605

b. If B represent the number of times an odd number comes up. For the fair die the probability that an odd number comes up is 0.5.

Thus B ~ Bin(8, 1/2 )

The probability mass function of the random variable B is given by

$p(B) = \left \{ {(8!)/(B!(8 - B)!)*((1)/(2) )^(B\n)*((1)/(2) )^(8-B) } \right. for B=0,1, ...8$

hence p(odd comes up 5 times) is

$p(x=5) = p(2)=(8!)/(5!3!) *((1)/(2) )^(5) *((1)/(2) )^(3)$

p(5) = 0.2188

c. let the mean no of times a 6 comes up be μₐ

and let the total number of outcomes be n

using the formula μₐ = nρₐ

μₐ = 8 * 1/6

= 1.33

d. let the mean nos of times an odd nos comes up beμₓ

let the total outcomes be n = 8

let the probability odd be pb = 1/2

μₓ = npb

= 8 * (1/2)

= 4

e. the standard deviation of a random variable A is given as follows

σₐ $= √(np(1-p))$

where p = 1/6 (prob 6 outcome)

n = total outcomes = 8

$= \sqrt{8*(1)/(6)*(5)/(6) }$

= 1.0540

f. the standard dev of the binomial random variable Y is given by

σ $= √(np(1-p))$

where p = 1/2 and n = 8

= $\sqrt{8*(1)/(2) *(1)/(2) }$

= 1.4142

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You are playing a video game. For each diamond you collect, you earn 110 points. You also earn 80 bonus points by completing the level in less than 2 minutes. You need to earn more than 1620 points to continue on to the next level. Write and solve an inequality that represents the numbers d of diamonds you must collect in less than 2 minutes to advance to the next level.

Answers

Answer:

110d=1620

Step-by-step explanation:

110d=1620

divide by 110 on each side

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During migration a butterfly can travel 30 miles in 1 hour. Which graph best represents y the number of miles a butterfly can travel in x hours

Answers

The linear equation that models this situation is y = 30x

What is an equation?

An equation is an expression showing the relationship between numbers and variables.

The slope intercept form of a straight line is:

y = mx + b

Where m is the slope and b is the y intercept.

The standard form of a straight line is:

Ax + By = C

Where A, B and C are constants

Let y represent the number of miles a butterfly can travel in x hours. The butterfly can travel 30 miles in 1 hour, hence:

y = 30x

The graph is attached

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Each prize for a carnival booth costs $0.32. How many prizes can you buy with $96?

Answers

Answer: 96 divided by 0.32 is 300, so it's 300.

Find the equation of the line through the points (-3,-3) and (2,-1) using point-slope form. Then rewrite theequation in slope-intercept form.

Answers

Answer: See below

Step-by-step explanation:

The point-slope equation is y-y₁=m(x-x₁). Since we don't know our slope, we can use the formula $m=(y_(2)-y_(1) )/(x_(2)-x_(1) )$ to find the slope. All we have to do is use the coordinate we were given and plug it into the formula.

$m=(-1-(-3))/(2-(-3)) =(2)/(5)$

Now that we have the slope, we can fill out the point-slope equation.

y-(-3)=2/5(x-(-3))

y+6=2/5(x+3)

This is the point-slope form.

Now, we can distribute and solve to get slope-intercept form.

y+6=2/5x+6/5

y=2/5x-24/5

Final answer:

The equation of the line through the points (-3,-3) and (2,-1) can be found using point-slope form. It is y = (2/5)x - 9/5 in slope-intercept form.

Explanation:

To find the equation of a line using the point-slope form, we need to determine the slope of the line and use one of the given points to write the equation. Firstly, let's find the slope of the line using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the coordinates (-3, -3) and (2, -1) into the formula gives us m = (-1 - (-3)) / (2 - (-3)) = 2/5. Now, we can choose one of the points (for example, (-3, -3)) and use the point-slope form equation: y - y1 = m(x - x1). Substituting the values, we get y - (-3) = (2/5)(x - (-3)). Simplifying the equation yields y + 3 = (2/5)(x + 3), which is the equation of the line in point-slope form.

To rewrite the equation in slope-intercept form y = mx + b, we need to isolate the y variable. Distributing the (2/5) to (x + 3) in the point-slope form equation gives us y + 3 = (2/5)x + 6/5. Subtracting 3 from both sides gives us y = (2/5)x + 6/5 - 3. Simplifying further, the equation becomes y = (2/5)x - 9/5. Therefore, the equation of the line through (-3, -3) and (2, -1) in slope-intercept form is y = (2/5)x - 9/5.

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Data sets A and B are dependent. Find mean of the differences (d bar).A 32 30 49 45 33
B 30 26 27 37 24
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Answers

Answer:

9.0

Step-by-step explanation:

Mean = Sum of terms/Number of terms

For Data Set A

Mean = 32 + 30 + 49 + 45 + 33/5

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For Data Set B

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Mean Difference = 37.8 - 28.8

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Answers

Answer:

{}

Step-by-step explanation:

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