Question Four

An academic conference held this past January consistent of 250 participants including undergraduate students, masters students, PhD students, and, professors from business faculties, engineering faculties, and nursing faculties to discuss various ways of increasing the learning desires of students. The following table gives us the breakdown of participants by levels of education and faculties.

                                                                Business               Engineering               Nursing                    Totals

Undergraduate students                     30                               15                               35                               80

Masters students                                    40                               38                               12                               90

PhD students                                             10                               12                               8                               30

Professors                                                  20                               15                               15                               50

Totals                                                        100                               80                               70                           250

1. The probability that this participant is from business is __ 100/250_____

2. The probability that this participant is a PhD student is __30/250____

3. The probability that this participant is a nursing professor is __15/50_____

4. The probability that this participant is either an undergraduate or a master’s student is _170/250_______

5. The probability that this participant is either from business or a PhD student is ________

6. The probability that this participant is a Professor knowing that he/she is in nursing is ________

7. The probability that this participant is from business knowing that he/she is a master’s student is

_____

Identify the Distribution

Select the Distribution that best fits the definition of the random variable X in each case.

1. Each hurricane independently has a certain probability of being classified as "serious." A climatologist wants to study the effects of the next 5 serious hurricanes. X = the number of non-serious hurricanes observed until the data is collected.

2. Ten percent of Netflix users watch a particular show. A survey asks 25 independent viewers whether they watch this show. X = the number who say yes.

3. The number of car accidents at a particular intersection occur independently at a constant rate with no chance of two occurring at exactly the same time. X = the number of accidents on a Thursday.

4. Potholes along a road occur independently at a constant rate with no chance of two occurring at exactly the same place. X = the distance between consecutive potholes.

5. Buses arrive at a certain stop EXACTLY every 15 minutes. You show up at this bus stop at a random time. Let X = your waiting time until the next bus.

6. A soccer player has a certain probability p of being injured in each game, independently of other games. X = the number of games played before the player is injured.

7. Proportions of individuals with tree blood types in a population are 0.2, 0.3 and 0.5 respectively. We select randomly 50 individuals from a large population. What is the joint distribution of the number of individuals in the sample with the first and second blood type, respectively?

8. A designer is working on a new ergonomic chair, and they want it to work best for average height people, so they measure the heights of all 50 people working in their office. Let X = the average height.

9. In Lotto 6/49 a player selects a set of six numbers (with no repeats) from the set{1, 2, ..., 49}. In the lottery draw, six numbers are selected at random. Let X = the first number drawn.

10. A tank contains 10 tropical fish, 2 of which are a rare species. Five fish are removed from the tank. X = the number of rare fish left in the tank.

This assignment is to give you practice using struts, arrays, and sorting. (Objective C++ and please have a screenshot of output)

In competitive diving, each diver makes dives of varying degrees of difficulty. Nine judges score each dive from 0 through 10 in steps of 0.5. The difficulty is a floating-point value between 1.0 and 3.0 that represents how complex the dive is to perform. The total score is obtained by discarding the lowest and highest of the judges’ scores, adding the remaining scores, and then multiplying that total by the degree of difficulty. Write a program to score each of the dives, using the following input and output specifications, and determine the winner of the competition.

Input:

Create the file m7dive.txt for input and the output must go to an output file named mp7output.txt.

The first line contains an integer for the number of divers in the competition and subsequent lines contain:
Diver’s name (10 characters max, no blanks included), difficulty (double), and judges’ ratings (nine doubles). There is one line of data for each diver.

Example file:

Output:

The name and difficulty, followed by the scores sorted into increasing order, in tabular form with appropriate headings along with the earned total points for that diver.

Example for sample output of the input file data above

The winner is Anne with the points of 124.0

At the end of the table, print out the name of the winner of the competition (the person with the highest points) and his/her final score.

Hint: You must use functions to modularize your program. Here is the full data of your input file mp7dive.txt, please send the output to an output file mp7output.txt.

The first line is 7 which is the number of divers in the file. The rest of the lines are as described above.

7
Anne          2.0   8.5  8.5  9.0   9.0   9.0   9.5  8.5  8.0  9.5
Sarah         1.6   7.5  8.5  8.0   8.0   7.0   9.0  8.5  8.5  8.0
Deborah   2.3   9.0  9.0   9.5  10.0 10.0 9.5  9.5   9.5  9.5
Kathryn     2.4   9.0  9.0  9.0   9.5   9.5    9.5  9.0  8.0  8.5
Jacquelin   2.7   9.0  9.0  9.5   9.5   9.0    8.5  8.5  8.5  9.5
Elizabeth   2.9   8.0  8.0  7.5   8.5   8.5    8.0  8.0  7.5  8.5
Tina           2.5   8.5  8.5  8.5   8.5   8.5    8.5  8.5  8.5   8.5

Using RStudio

15. (9 pts) A particular basketball player has a season long free throw percentage of 55%. The player takes 7 free throws.

a) Explain why this is a binomial probability.

b) Create a table with the probability distribution.

c) Create the histogram for the probability distribution.

A surgeon performs 5 surgeries in a week. Each surgery has 0.1
probability of developing complications. If the surgeries are
independent find:
a. The probability all 5 surgeries develop complications
b. The probability at least one of the surgeries develop
complications.
c. Exactly two of the surgeries develop complications

Consider the probability that more than 43 out of 130 people have been in a car accident. Assume the probability that a given person has been in a car accident is 3%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

Yes or No

Let X be a continuous random variable with a probability density function fX (x) = 2xI (0,1) (x) and let it be the function´ Y (x) = e −x

a. Find the expression for the probability density function fY (y).

b. Find the domain of the probability density function fY (y).