Tanya enters a raffle at the local fair, and is wondering what her chances of winning are. If her probability of winning can be modeled by a beta distribution with α = 5 and β = 2, what is the probability that she has at most a 10% chance of winning?

Answers

Answer 1

Answer:

Answer:

$P(X<0.1)= 5.5x10^(-5)$

Step-by-step explanation:

Previous concepts

Beta distribution is defined as "a continuous density function defined on the interval [0, 1] and present two parameters positive, denoted by α and β, both parameters control the shape. "

The probability function for the beta distribution is given by:

$P(X)= (x^(\alpha-1) (1-x)^(\beta -1))/(B(\alpha,\beta))$

Where B represent the beta function defined as:

$B(\alpha,\beta)= (\Gamma(\alpha)\Gamma(\beta))/(\Gamma(\alpha+\beta))$

Solution to the problem

For our case our random variable is given by:

$X \sim \beta (\alpha=5, \beta =2)$

We can use the following R code to plot the distribution for this case:

> x=seq(0,1,0.01)

> plot(x,dbeta(x,5,2),main = "Beta distribution a=5, b=2",ylab = "Probability")

And we got as the result the figure attached.

And for this case we want this probability, since we want the probability that she has at most 10% or 0.1 change of winning:

$P(X<0.1)$

And we can find this probability with the following R code:

> pbeta(0.1,5,2)

[1] 5.5e-05

And we got then this : $P(X<0.1)= 5.5x10^(-5)$

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Grayson bought snacks for his teams practice. He bought a bag of popcorn for $3.50 and a five pack of juice bottles. The total cost before tax was $11.05. Right and solve an equation which can be used to determine J, how much each bottle of juice cost.

Answers

The each bottle of juice cost $ 7.55 before tax .

What is arithmetic?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Grayson bought bag of popcorn (P)= $3.50

Five pack of juice bottles.

The total cost before tax was $11.05.

According to given question we have

Let the cost of the juice bottles be x.

P+ x= $11.05.

$3.50+x=$11.05

x=$11.05-$3.50

x=$ 7.55

Therefore, the each bottle of juice cost $ 7.55 before tax .

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Final answer:

The question is about finding the cost of each bottle of juice. The cost of the juices was found by subtracting the cost of popcorn from the total amount. Each bottle of juice cost $1.51.

Explanation:

To solve this problem, we need to first determine how much was spent on the juice. We know that Grayson spent $11.05 in total and that the popcorn cost $3.50. By subtracting the cost of the popcorn from the total spent, we will find out how much Grayson spent on the juice.

Step 1: Subtract the cost of the popcorn from the total amount spent: $11.05 - $3.50 = $7.55. This is how much was spent on the juice bottles.

Step 2: We know that there are five juice bottles in the pack. To find out the cost of each juice bottle (J), we divide the total cost of the juice by the number of bottles in the pack: $7.55 / 5 = $1.51.

So, the equation which determines J, the cost of each juice bottle, is $3.50 + 5J = $11.05. Solving this equation gives J = $1.51.

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What is the slope intercept form equation of the line that passes through (3, 4) and (5, 16)?

Answers

It is convenient to start with the 2-point form of the equation for a line.

... y - y1 = (y2 - y1)/(x2 - x1)×(x - x1)

Either point can be (x1, y1), and the other can be (x2, y2). If we take them in order, we get

... y - 4 = (16 - 4)/(5 - 3)×(x - 3) . . . . . fill in the two points

... y = 12/2(x -3) +4 . . . . . . . . . . . . . . add 4, simpliffy a bit

... y = 6x -18 +4 . . . . . . . . . . . . . . . . . eliminate parentheses

... y = 6x -14 . . . . . . . . . . . . . . . . . . . . put in slope-intercept form

What is the volume of the cone below

Answers

Answer:

263.99Pi or 264Pi units by approximation

Step-by-step explanation:

Volume of cone is 1/3 x Pi x radius ^2 x height

Radius is given as 6, height as 22

Hence volume of cone= 1/3 x Pi x (6)^2 x 22

=1/3 x PI x36x 22

= 263.99 PI

=264PI units

Two chocolate donuts have about400 calories. How many calories
would you expect to be in
5 chocolate donuts?

Answers

Answer:

1000 calories

Step-by-step explanation:

You can assume that each chocolate donut is 200 calories by doing 400/2, from there you do 200 times 5, which gets you 1000

Answer:

Step-by-step explanat

about 1000 i multipy 200X5

A welding drawing shows that the weld-root reinforcement cannot exceed " in thickness. Your weld measurement tools are metric, so this value needs to be converted to millimeters. You know that one inch equals 2.54 centimeters. What is the maximum weld-root reinforcement allowed in millimeters? Round your answer to the nearest tenth of a millimeter.

Answers

Answer:

3.2 millimeters

Step-by-step explanation:

1/8*2.54 *10 = 3.175

= 3.2 millimeter. (rounded to nearest tenth)

Final answer:

To convert the thickness from inches to millimeters, the given value (in inches) should be multiplied by 25.4 and the result rounded to the nearest tenth of a millimeter.

Explanation:

The subject of this question is a conversion of units from inches to millimeters. In such conversions, one of the basic knowledge is that 1 inch is equivalent to 2.54 centimeters (cm). However, in this case, we need the answer in millimeters (mm), not cm. Keep in the back of your mind that 1 centimeter (cm) is equal to 10 millimeters (mm). This means, 1 inch will be equivalent to 2.54 cm, which further converts to 25.4 mm.

To find out the maximum value of weld-root reinforcement in millimeters, we simply need to apply the conversion factors. To convert the given thickness in inches to millimeters, you multiply the given value (in inches) by 25.4. Round your answer to the nearest tenth of a millimeter.

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Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 139 millimeters, and a variance of 49. If a random sample of 34 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 1.8 millimeters

Answers

The probability that the sample mean would differ from the population mean by more than 1.8 millimeters is approximately 0.0668.

What is the standard deviation?

A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.

The standard deviation of the population is $√(49) = 7$ millimeters. The standard error of the sample mean is then

$(7)/(√(34)) = (7)/(5.874) \approx 1.2$ millimeters.

The probability that the sample mean would differ from the population mean by more than 1.8 millimeters is the probability that it falls outside of the interval $(139 - 1.8, 139 + 1.8)$ . We can use the standard normal distribution to approximate this probability.