In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. Furthermore, there is a weight limit of 2500 lb. Assume that the average weight of students, faculty, and staff on campus is 154 lb, that the standard deviation is 27 lb, and that the distribution of weights of individuals on campus is approximately normal. If a random sample of 16 persons from the campus is to be taken:

What is the expected value of the sample mean of their weights?
μ_x =  lb

(b) What is the standard deviation of the sampling distribution of the sample mean weight? (Round your answer to two decimal places.)
σ_x =  lb

(c) What average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lb? (Round your answer to two decimal places.)
x >  lb

(d) What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit? (Round your answer to four decimal places.)
P =

JAVA code

Create a new class called BetterDiGraph that implements the EditableDiGraph interface See the interface below for details.

EditableDigraph below:

import java.util.NoSuchElementException;

/**
* Implements an editable graph with sparse vertex support.
*
*
*/
public interface EditableDiGraph {
  
/**
* Adds an edge between two vertices, v and w. If vertices do not exist,
* adds them first.
*
* @param v source vertex
* @param w destination vertex
*/
void addEdge(int v, int w);

/**
* Adds a vertex to the graph. Does not allow duplicate vertices.
*
* @param v vertex number
*/
void addVertex(int v);

/**
* Returns the direct successors of a vertex v.
*
* @param v vertex
* @return successors of v
*/
Iterable getAdj(int v);
  
/**
* Number of edges.
*
* @return edge count
*/
int getEdgeCount();
  
/**
* Returns the in-degree of a vertex.
* @param v vertex
* @return in-degree.
* @throws NoSuchElementException exception thrown if vertex does not exist.
*/
int getIndegree(int v) throws NoSuchElementException;
  
/**
* Returns number of vertices.
* @return vertex count
*/
int getVertexCount();
  
/**
* Removes edge from graph. If vertices do not exist, does not remove edge.
*
* @param v source vertex
* @param w destination vertex
*/
void removeEdge(int v, int w);

/**
* Removes vertex from graph. If vertex does not exist, does not try to
* remove it.
*
* @param v vertex
*/
void removeVertex(int v);

/**
* Returns iterable object containing all vertices in graph.
*
* @return iterable object of vertices
*/
Iterable vertices();

/**
* Returns true if the graph contains at least one vertex.
*
* @return boolean
*/
boolean isEmpty();
  
/**
* Returns true if the graph contains a specific vertex.
*
* @param v vertex
* @return boolean
*/
boolean containsVertex(int v);
}

A survey on the number of hours a college student works per week showed that the hours varied from 5 to 61 where 5 was the lowest number and 61 was the highest number. Determine the class width, classes, class marks and class boundaries of a frequency distribution table if the work hours were grouped using 8 classes. You can make a table to help you do this. Note: there is no frequency column.

Number Analysis Program Python:

Initialize an array with these specific 20 numbers: 26 45 56 12 78 74 39 22 5 90 87 32 28 11 93 62 79 53 22 51

Display the following data:

1. The lowest number in the list
2. The highest number in the list
3. The total of the numbers in the list
4. The average of the numbers in the list

A random number generator picks a number from 7 to 68 in a uniform manner. Round answers to 4 decimal places when possible.

1. The mean of this distribution is
2. The standard deviation is
3. The probability that the number will be exactly 42 is P(x = 42) =
4. The probability that the number will be between 16 and 28 is P(16 < x < 28) =
5. The probability that the number will be larger than 48 is P(x > 48) =
6. P(x > 18 | x < 50) =
7. Find the 61st percentile.
8. Find the minimum for the lower quartile

A random number generator picks a number from 18 to 64 in a uniform manner. Round answers to 4 decimal places when possible.

The mean of the distribution is:

The standard deviation is:

The probability that the number will be exactly 20 is P(x = 20) =

The probability that the number will be between 24 and 26 is P(24 < x < 26) =

The probability that the number will be larger than 32 is P(x > 32) =

P(x > 19 | x < 51) =

Find the 79th percentile.

Find the minimum for the upper quartile.

The accompanying table describes the random variable​ x, the numbers of adults in groups of five who reported sleepwalking. Complete parts​ (a) through​ (d) below. LOADING... Click the icon to view the table. a. Find the probability of getting exactly 4 sleepwalkers among 5 adults. nothing ​(Type an integer or a decimal. Do not​ round.) b. Find the probability of getting 4 or more sleepwalkers among 5 adults. nothing ​(Type an integer or a decimal. Do not​ round.) c. Which probability is relevant for determining whether 4 is a significantly high number of sleepwalkers among 5​ adults: the result from part​ (a) or part​ (b)? A. Since the probability of getting 4 sleepwalkers is the result from part​ (a), this is the relevant probability. B. Since the probability of getting 5 sleepwalkers includes getting 4​ sleepwalkers, the result from part​ (b) is the relevant probability. C. Since the probability of getting 5 sleepwalkers is less likely than getting 4​ sleepwalkers, the result from part​ (a) is the relevant probability. D. Since the probability of getting fewer than 4 sleepwalkers is the complement of the result from part​ (b), this is the relevant probability. d. Is 4 a significantly high number of 4 sleepwalkers among 5​ adults? Why or why​ not? Use 0.05 as the threshold for a significant event. A. ​No, since the appropriate probability is less than​ 0.05, it is not a significantly high number. B. ​No, since the appropriate probability is greater than​ 0.05, it is not a significantly high number. C. ​Yes, since the appropriate probability is less than​ 0.05, it is a significantly high number. D. ​Yes, since the appropriate probability is greater than​ 0.05, it is a significantly high number. Click to select your answer(s).

x ​P(x) 0 0.171,

1 0.355

2 0.304

3 0.138

4 0.028

5 0.004

You have a competition with your friend to see who can get the first free-shot into the basket. Your free-throw percentage is 0.25, whereas your friend’s free-throw percentage is 0.33.

a) On average, how many free-throw attempts do you need to make in order to achieve the first free-throw in the basket?

b) On average, how many free-throw attempts does your friend need to make in order to achieve the first free-throw in the basket?

c) Compute the probability that the bet ends at or before you both make 10 free-throw attempts.

d) Compute the probability of a tie, assuming that the game ends at or before 10 free-throw attempts.

e) Compute the probability that you win the bet, assuming that the game ends at or before 10 free-throw attempts.

f) Assume that you will pay your friend $1, if he wins, $0 in the case of a tie, and he pays you $x if you win the bet. Compute the minimum $x you would accept for this bet to be profitable in the long run?

Recall from class that P(X>n)=(1-p)n when X~Geom(p).