Suppose that the length of research papers is uniformly distributed from 12 to 25 pages. We survey a class in which 55 research papers were turned in to a professor. The 55 research papers are considered a random collection of all papers. We are interested in the average length of the research papers.
A.) Give the distribution of X. (round your standard deviation to two decimal places. X
∼ N (18.5, _____)
B.) Give the distribution of SumX. Round your standard deviation to two decimal places. SumX
∼ (1017.5, _____).
C). Calculate the probability that the professor will need to read a total of more than 1080 pages. _____

Answer:

A.) X ~ N(18.5, 3.75)

B.) SumX ~ N(1017.5,27.8).

C.) 0.0122 = 1.22% probability that the professor will need to read a total of more than 1080 pages.

Step-by-step explanation:

Uniform distribution:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b.

The mean is given by:

[tex]M = \frac{a+b}{2}[/tex]

The standard deviation is given by:

[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]

Normal probability distribution

When the distribution is normal, we use 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.

The uniform distribution can be approximated to the normal, using its mean and its standard deviation.

Sum of n terms of a normally distributed variable:

The mean of the sum will be:

[tex]\mu_{s} = n\mu[/tex]

The standard deviation of the sum will be:

[tex]\sigma_{s} = \sqrt{n}\sigma[/tex]

Suppose that the length of research papers is uniformly distributed from 12 to 25 pages.

This means that [tex]a = 12, b = 25[/tex]

We survey a class in which 55 research papers were turned in to a professor.

This means that [tex]n = 55[/tex]

A.) Give the distribution of X.

The mean has already been given, and the standard deviation is:

[tex]S = \sqrt{\frac{(25-12)^2}{12}} = 3.75[/tex]

So

X ~ N(18.5, 3.75)

B.) Give the distribution of SumX.

Sum of 55 papers, the standard deviation will be of:

[tex]\sigma_{s} = \sqrt{55}*3.75 = 27.8[/tex]

So

SumX ~ N(1017.5,27.8).

C). Calculate the probability that the professor will need to read a total of more than 1080 pages

This is 1 subtracted by the pvalue of Z when X = 1080. So

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

[tex]Z = \frac{1080 - 1017.5}{27.8}[/tex]

[tex]Z = 2.25[/tex]

[tex]Z = 2.25[/tex] has a pvalue of 0.9878

1 - 0.9878 = 0.0122

0.0122 = 1.22% probability that the professor will need to read a total of more than 1080 pages.

If 30 pounds of rice and 30 pounds of potatoes cost $33.60 and 20 pounds of rice and 12 pounds of potatoes costs $19.04, how much will 10 pounds of rice and 50 pounds of potatoes cost?

A group of friends wants to go to the amusement park. They have no more than $275

to spend on parking and admission. Parking is $17.50, and tickets cost $25 per

person, including tax. Write and solve an inequality which can be used to determine

2, the number of people who can go to the amusement park.

Is the graph increasing, decreasing, or constant?
O A. Constant
O B. Increasing
C. Decreasing

The number of hospitals in a certain country has been declining for many years. In 2014, there were 5,727 hospitals, but, in 2017, there were only 5,571. Assuming this trend is linear, write an equation for the number of hospitals H in the this country t years since 2000.
H=

WILL MARK BRAINLIEST

The Miller family and the Adams family both purchased houses on the same day several years ago
The Miller family bought their house for S159,352 and it has been increasing in value by 3.7% each year.
The value of the Adams family's home since it was purchased, A(z) can be modeled by the function A(z) = 142, 809(1.04)", where a represents the number of years since the house was purchased
PartA) Which family paid more for their house?
Part B) Which family's home value is increasing at a faster rate?

Which expression results from using the Distributive Property?
16. 3(6 +r)
A. 6+r
B. 6 + 3r
C. 181
D. 18 + 3r

PLEASE HELP ASAP!!!!

Tyra made 8 fewer jackets than zack they made 48 jackets altogether how many jackets did zac make

g The population of Little Townville in 2005 was 13,625 people. In 2009 the population grew to 15,325 people. Assume that this trend is linear and the population has been growing like this since 2000. a. Write a function for the population, P, in terms of the number of years since 2000, ????. (6 points) b. What is the slope of the function and what does it represent in the context of the problem. Include units. (5 points) c. What is the vertical intercept of the function and what does it represent? Include units (5 points) d. What do you believe the population was in 2015?

What is the value of the expression below? |6| + |-4|​

1) Ellen Murphy manages an Auto Film outlet that

applies window films to automobile windows.

She reported that last week a total of 28 autos had

window film applied. Auto Film charges $129.99

for a four-door sedan and $99.99 for a two-door

coupe. If Ellen had total receipts for the week of

$3,459.72, how many four-doors sedans had been

serviced? How many two-door coupes?

how do I solve this puzzle? ​

3. Paulo can jog 20 miles in 5 hours. At this rate, how many miles can Paulo jog in 4 hours? *​

A=6
B=8
The measure of c is

Briana used two congruent parallelograms and a square to create the figure shown. What is the areaa of the figure Briana created in square feet?

A. 27ft²
B.24 3/4 ft²
C.67 1/2 ft²
D.33 3/4 ft²​

What is the slope of the line that passes through the points (-4, 8) and (-14, 8) ? Write your answer in simplest form.

8m/3 if m = 12
Evaluate

What is the product?
(X^4)(3x-2)(4x2 +5x)?

PLEASE HELP!!! DUE SOON!!!

Who dunnit in math there is 10 problems

please help geometry

question is down below thanks

Janel has $250 in her bank account and is earning $75 a week babysitting the annoying neighbor kids. April has $720 in her bank account and spends $35 a week on clothes and shoes. how long will it take for the two to have the same amount of money in their bank accounts? solve using systems of equations.

Translate the given phrase into an algebraic expression and simplify if possible: the sum of -4 and the difference of 3 and 1

Beach balls are very popular at
Sam's Swim Shop. He decides to
begin charging 40% more. If he
originally charged $5.50, by how
much will he increase the price?

Question 16
If n = 6, what is the value of 9n – 4?
Α.
11
B.
50
С
52
D
54

find the equation of the line passing through (2,3) and (1,5)

6xy^3 * 4x^2y^2 answer​

A dog is tied with a rope to a stake in the ground. The length of the rope is 10 yards.
What is the area, in square yards, in which the dog can roam?
1) 1001
2) 100x yd.2
3) 100 yd.2
4) 20ryd.

Can someone tell me how to do this task please?

The area of a rectangle is 36 square inches, and its perimeter is 26 inches. What are the length and width of the rectangle?