The data base regarding the billing rates of K-Electric in lower earning areas of the Karachi shows the average billing for the electricity is normally distributed with an average of Rs.1100 with a standard deviation of Rs.100. If the bills are measured to the nearest Rs.50 find the probability that the next bill will contain                                                                                  

1. Below Rs.1090
2. Exactly Rs.1120
3. At least Rs.1110
4. Between 1270 and 1350 inclusive
5. Find the highest value of x having 15% of the bills having amount below that

A survey showed that 84% of adults need correction eyeglasses, contacts, surgery, etc.) for their eyesight lf 9 adults are randomly selected find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight correction?
The probability that no more than 1 of the 9 adults require eyesight correction is _____ (Round to three decimal places as needed.)

Is 1 a significantly low number of adults requiring eyesight correction? Note that a small probability is one that is less than 0.05

A. No, because the probability of this occurring is small.
B. No, because the probability of this occurring is not small.

C. Yes, because the probability of this occurring is small.
D. Yes, because the probability of this occurring is not small.

This project involves writing a program to simulate a blackjack card game. You will use a simple console-based user interface to implement this game. A simple blackjack card game consists of a player and a dealer. A player is provided with a sum of money with which to play. A player can place a bet between $0 and the amount of money the player has. A player is dealt cards, called a hand. Each card in the hand has a point value. The objective of the game is to get as close to 21 points as possible without exceeding 21 points. A player that goes over is out of the game. The dealer deals cards to itself and a player. The dealer must play by slightly different rules than a player, and the dealer does not place bets. A game proceeds as follows: A player is dealt two cards face up. If the point total is exactly 21 the player wins immediately. If the total is not 21, the dealer is dealt two cards, one face up and one face down. A player then determines whether to ask the dealer for another card (called a “hit”) or to “stay” with his/her current hand. A player may ask for several “hits.” When a player decides to “stay” the dealer begins to play. If the dealer has 21 it immediately wins the game. Otherwise, the dealer must take “hits” until the total points in its hand is 17 or over, at which point the dealer must “stay.” If the dealer goes over 21 while taking “hits” the game is over and the player wins. If the dealer’s points total exactly 21, the dealer wins immediately. When the dealer and player have finished playing their hands, the one with the highest point total is the winner. Play is repeated until the player decides to quit or runs out of money to bet. You must use an object-oriented solution for implementing this game.

Each public class must be contained in a separate Java source file. Only one source file will have a main() method and this source will be named BlackjackGameSimulator.java. Other source/class names are up to you following the guidelines specified so far in the course. The format of the Java source must meet the general Java coding style guidelines discussed so far during the course. Pay special attention to naming guidelines, use of appropriate variable names and types, variable scope (public, private, protected, etc.), indentation, and comments. Classes and methods should be commented with JavaDoc-style comments (see below). Please use course office hours or contact the instructor directly if there are any coding style questions. JavaDocs: Sources should be commented using JavaDoc-style comments for classes and methods. Each class should have a short comment on what it represents and use the @author annotation. Methods should have a short (usually 1 short sentence) description of what the results are of calling it. Parameters and returns should be documented with the @param and @return annotations respectively with a short comment on each. JavaDocs must be generated against every project Java source file. They should be generated with a - private option (to document all protection-level classes) and a –d [dir] option to place the resulting files in a javadocs directory/folder at the same level as your source files.

Consider successive flips of a coin that always lands on "heads" with probability p, and determine the probability distribution of the first time, after the beginning, that the total number of heads is equal to the total number of tails. Hint: the first time that this occurs is at time 2n can be obtained by first conditioning on the total number of heads in the first 2n trials.

A cloud computing provider has 475 customers and a farm of 250 compute servers each having 4 cores. The company statistics indicate that at the peak hour the workload requirements of its customers are such that each requires {0,1,2,3,4} cores with uniform probability. Use the approximation based on Central Limit Theorem to answer the following questions.

1. Compute the outage probability, i.e., the probability that there are not a sufficient number of cores to meet customers demands.

2. The company decides to offer its customers a new super fast service which would speed up their quality of service by automatically doubling the number of cores allocated to each customer. Each customer would thus be allocated {0,2,4,6,8} cores with uniform probability. How many extra (4 core) machines should you need to buy in order support new service while maintaining the same outage probability ?

3. The server vendor is quite happy to sell you the number of 4 core servers determined in the previous question, but offers you a great deal on the same number of 8 core servers. If you purchased the same number of servers but now with 8 cores, how many super fast customers could you support same outage probability?

C++

Code each of the following functions RECURSIVELY  (each function should use only the parameter value, and any local function variables you might need ..no variables are to be declared outside the functions).

void upTo(int number)

This function prints all values from 1 up to the number.

upTo(5);

should output: 1 2 3 4 5

HINT: the following functions involve separating a digit from a number. Use of the arithmetic operators % and / are helpful here. Remember a % 10 results in the leftmost digit of a number, and a = a / 10 removes the leftmost digit from a number.

void printRev(int number)

This function prints out the digits of the parameter in reverse. For example, the call    

printRev(2367);    will print out     7632

int sumDig(int number)

This function returns the sum of the digits in the parameter. For example, the call             

cout << sumDig(4372);    will print out the value 16.

bool isThere(int number, int digit)

This function returns true if digit occurs in number, and false otherwise.

For example, the following statement will print “it is there”.

             if ( isThere(4593, 9) )

                     cout << “it is there”;

             else

                     cout<< “it is not there”;

int howmany(int number, int digit)

This function returns the number of occurrances of 'digit' in the parameter number.

For example, the following statement will print 3

cout << howmany(22542, 2) << endl;

* prompt the user for a positive integer

* call upTo, sumDig, printRev

* prompt the user for a single digit

* call isThere using this integer (and digit) as parameter values

* call howmany using this integer the digit as parameter values

1. In 1994, baseball management and the players union failed to come to an agreement and the management initiated a work stoppage. The two sides did not come to an agreement until 1995. As a result less baseball games were played in both the 1994 and 1995 season. The 1994 and 1995 data seem to be outside the pattern of the rest of the data. Determine if these two data points are influential by:

a) Plot the regression line from the full data set on the on the scatter plot. The regression equation is: Wins = 24.5 + 0.08Runs, mark it “ALL SEASONS”

b) ​​​​​​​Plot the regression line from data set without the partial seasons on the on the scatter plot. The regression equation is: Wins = 43.3 + 0.05RUNS, mark it “ONLY FULL SEASON”. Do the partial seasons seem to be influential? Explain.

c) Using the linear regression model for “ALL GAMES” in the Red Socks data, Wins = 24.5+ 0.08 Runs. Consider the data for the year 2004, (Runs = 949, Wins = 98) Calculate the residual for this year.

d) The coefficient of determination = 67.2% for the Red Socks data. Find the linear correlation coefficient. Round your answer to 2 decimal places.

sume that a procedure yields a binomial distribution with nequals4 trials and a probability of success of pequals0.40. Use a binomial probability table to find the probability that the number of successes x is exactly 2.

Suppose a single fair die is rolled.

Find the probability that it is a 2, given that it is an odd number.

The probability is

In a particular city, the average number of live births every month is seven. Assume that the number of births follows a Poisson distribution.

1. What is the probability that no live births will occur during the month of February?

2. What is the probability that at least five live births occur during the month of June?

3. What is the probability that six or more live births will occur during the month of June?

4. What is the probability that seven live births will occur during the month of March?