1.You attend a public health conference for student research. You count 23 posters presented by undergraduate students and 46 posters presented by graduate students. Out of all the posters, 15 posters included research on infant health concerns, 28 focused on young adult health concerns, and 14 discussed health concerns for senior citizens.

You pick a random poster to read. What is the probability you pick a poster presented by a graduate student?

What is the probability you pick a poster discussing young adult health concerns?

2.Use the standard normal distribution to calculate the following probabilities:

Cumulative area to the left:

P (z < 1.20) =

P (z < -1.09) =

P (z < 2.34) =

Cumulative area to the right:

P (z > 1.23) =

P (z > -2.05) =

P (z > 3.50) =

Subtracting cumulative areas:

P (-1.23 < z < 1.23) =

P (1.55 < z < 2.25) =

P (-3.50 < z < 2.50) =

3.An I.V. bag dispenses between 500 ml and 1000 ml of fluid, following a uniform distribution.

a.            Draw the distribution below. Include the probability function (the answer to 3b).

b.            What is the probability function for the amount of fluids dispensed?

c.             What is the probability that the amount of fluids dispensed will be less than 750 ml?

d.            What is the probability that the amount of fluid dispensed will be between 500 ml and 1000 ml?

e.            What is the probability that the amount of fluid dispensed will be between 600 ml and 800 ml?

4.I recently asked 100 middle school students to complete a statistics test. The mean score on the test was 30 points with a standard deviation of 5 points. The scores followed a normal distributions. Using this information, calculate the following:

a.            What is the probability a student earned a score of 45 points or less?

P (score < 45 points) =

b.            What is the probability a student earned a score higher than 30 points?

P(score > 30) =

c.             What is the probability a student earned a score between 25 and 45 points?

P (25 points < score < 45 points) =

d.            I want to know the cutoff value for the upper 10%. What score separates the lower 90% of scores from the upper 10%?

P (score < _______) = 90% or 0.90 cumulative area to the left

e.            I want to know the cutoff values for the lowest 25%.

P (score < ________) = 25% or 0.25 cumulative area to the left

f.             I would also like to know the cut off values for the highest 25%.

P (score > _______) = 25% or 0.25 cumulative area to the right

Write a C++ Program that does the following:

As you can see, there is a file named "invoice1_test1.txt". You are to use this file as your input file for your program. Do the following:

1. Sort the file by last name using an array. You can use any of the sorting algorithms we have previously used in class. You may use the string data type to store text data.

2. Compute the following:
a. The total balance due using the BalanceDue column.
b. Find the customer(s) with the highest number of rental days.
c. Find the customer(s) with the highest balance due.

Here's the file

invoice1_test1.txt

LastName FirstName DaysofRental BalanceDue
Smith Joe 15 100.50
Doe John 10 95.20
Anderson Paul 30 20.00
ODonell Miriam 10 24.30
Foster Sam 30 15.00
Zom Pete 10 20.00
Mock Chilly 100 30
Smitty Chris 200 200
Xu Conor 1 200
Anilo Steve 0 0

I have a hard time understanding the subject of fictitious forces. Let's discuss a few examples:

1) I'm sitting inside a vehicle which is accelerating in a straight line. I feel like someone is pushing me to the seat. So, on the one hand, I'm told that this happens according to the third Newton's law: this pressure is the result of me pushing the seat as a reaction to the seat pushing me (because it is accelerating with the same acceleration as the car). On the other hand, these forces are acting on different objects and I'm told that there is another fictitious force acting on me in an opposite direction to the acceleration. So what is right? And if there is a fictitious force, then why some call it a "math trick" when they are real and I can feel them?

2) I do not understand why some call centrifugal force a fictitious force. The earth is pulling the earth with its "invisible" string called gravitation. That's why the moon is still there. And this is the centripetal force. However the moon is also pulling the earth according to the Newton's third law, and that's why we have tides. This is the centrifugal force. So why it is fictitious? What it has to do with frame of reference? When we observe this in non-inertial frame of reference (such as the moon), does it simply mean that we can't call it anymore a reaction force according to the Newton's third law? But why if it is virtually the reaction force?

3) Accelerating elevator - similar to the first example - let's say the elevator is accelerating upwards. So we get that N? =m(g+a), and that's the same as me pushing the floor. That is why I feel heavier. Then why some add to here the fictitious force?

I will appreciate any answer.

In probability theory, a conditional probability measures the probability of an event given another event has occurred. The conditional probability of A given B, denoted by P(A|B), is defined by P(A|B) = P(A ∩ B) P(B) , provided P(B) > 0. Show that the conditional probability defined above is a probability set function. That is show that a) P(A|B) ≥ 0 [4 Marks] b) P(S|B) = 1. [4 Marks] c) P( S Ai |B) = PP(Ai |B) [4 Marks]

Use Excel/Megastat to find the discrete probability and cumulative probability of the Binomial distribution with probability of success p = 0.3 and n = 70.

Find its mean and variance.

Based upon the chart on Excel, what can you conclude about the binomial convergence?

Use binom.dist function on Excel and sketch the curve.

World Religion

Islam rejects Christian teaching that all humans are born sinners. Rather, each person freely chooses to follow God and do good or not. For Islam, the Christian doctrine of original sin removes personal responsibility. The idea that Jesus died for others is judged to be unfair and against God’s justice. Each individual alone, is responsible for their eternal destiny.

Does the Christian or Muslim view of the human person and the role in their salvation make more sense? Why?

A sample of 449 government employees and some number of respondents from private corporations answered the question about their education in 2018. Compare their average highest year of school completed and answer the question: Did government employees on average have more education than private employees in the U.S. in 2018? Explain why you think so. [Do not run the test in SPSS. Use the SPSS output below.]

T-Test

1. Calculate the values to put into two blanks (----). [See the output above].

2. State the null hypothesis (in words).

3. State the research (one-tailed) hypothesis (in words). [Hint: inspect the sample means for stating correct direction].

4. Find t_critical for one-tailed test.

5. Based on this SPSS output at the 0.05 significance level do you reject or accept the null hypothesis? Why?

6. Based on this SPSS output at the 0.05 significance level, do you reject or accept the one-tailed research hypothesis?

7. Answer the problem’s question.

Which of the following statements are true for an atom with 3 energy levels? You can choose more than one answer.

When atomic electrons are excited to a higher level, they always return to their lowest energy level by jumping down one level at a time.

For a given battery voltage the kinetic energy of the free electron at the point of collision is higher if the atom is closer to the source of electrons.

When a free electron hits an atom, the atom is always excited to the highest energy level possible.

For a given position of the atom, the kinetic energy of a free electron at the point of collision increases as the voltage of the battery increases.

The number of different wavelengths emitted by the atom depends on the number of free electrons passing through the lamp.

The number of different wavelengths emitted by the atom depends on how much kinetic energy the free electron has when it hits the atom.

Photons are emitted as electrons in the atom jump up in energy.

Two dice are rolled. Let the random variable X denote the number that falls uppermost on the first die and let Y denote the number that falls uppermost on the second die.

(a) Find the probability distributions of X and Y.

(b) Find the probability distribution of X + Y.

4. Customers at a Post Office line up to transact business with a single clerk at the Postal Agency. Customers arrive at the rate of four per minute, following a Poisson distribution. The single Postal clerk takes 12 seconds to service a customer, following an exponential distribution.
   1. What is the probability that there are more than two customers in the system?
   2. What is the probability that the system is empty?
   3. How long will the average customer have to wait before reaching the Postal clerk?
   4. What is the expected number of customers in the queue?
   5. What is the average number in the system?
   6. If a second Postal Clerk is added (who works at the same pace), how will the operating characteristics computed in (b), (c), (d), and (e) change?