. A web-based algorithm classifies emails as spams or no-spam at a success rate of 70% of detecting a spam. A. Find a 95% confidence interval for the number of spam emails expected within a sample of 100 emails. B. Find a 95% confidence interval for the accuracy (standard deviation) of the detected number of spams within the 100 emails. C. Determine the probability that at least 85 emails out of 100 emails are spams. D. If for the 100 emails above, there was indeed actually 85 spam emails, test the claim that the same algorithm can still detect at least 85 emails with a 95% confidence.

According to the National Eye Institute, 8% of men are red-green colorblind. A sample of 125 men is gathered from a particular subpopulation, and 13 men in this sample are colorblind.

a. Is this statistically significant evidence that the proportion of red-green colorblind men is greater than the subpopulation than the national average with alpha = 0.05?

b. What is the maximum number of men that could have been colorblind in this sample that would lead you to fail to reject the null hypothesis?

c. Using 8% as the probability of being colorblind, find a 95% confidence interval for the number of men in a sample of 125 who are colorblind.

The following table is used for a number of questions below. The table above shows the responses of a survey of teenagers aged 14-18 when asked at what age they thought they would become financially independent.

1. What do the teens expect is the probability of being financially independent before age 25?
2. A recent Gallup poll found that only 14 percent of 24- to 34-year-olds are financially independent. Do teens have realistic expectations?

There are six blue balls and four red balls in the pocket. Take out a ball at random, check the color and put it back in the pocket.
1. If you take the ball out until the red one comes out, what is the probability that the ball will be drawn exactly five times and the experiment is over?
2. What is the average and variance of the number of times X is taken if the ball is pulled out until the red ball comes out?
3. Repeat the procedure ten times to remove the ball from the pocket. Find the mean and variance of the number of blue balls taken Y.

Given the following probability distributions for variables X and Y:

P(x, y)X                  Y

0.4       100            200

0.6       200            100

a. E(X) and E(Y).

b. σX and σY.

c. σXY. d. E(X + Y).

e. Suppose that X represents the number of patients successfully treated for Malaria and Y represents the number of patients successfully treated for Tuberculosis. And medication A (first row in the table) has a 40% of effectiveness and medication B (second row in the table) has a 60% of effectiveness. Interpret and make statements based on the calculations you did.

A finance journal published a study of whether the decision to invest in the stock market is dependent on IQ. Information on a sample of 156905 adults living in Finland formed the database for the study. An IQ score​ (from a low score of 1 to a high score of​ 9) was determined for each Finnish citizen as well as whether or not the citizen invested in the stock market. The following table gives the number of Finnish citizens in each IQ​ score/investment category. Suppose one of the 156905 citizens is selected at random. Complete parts a through f.

a. What is the probability that the Finnish citizen invests in the stock​ market?

The probability is ________.. ​(Round to the nearest thousandth as​ needed.)

b. What is the probability that the Finnish citizen has an IQ score of 6 or​ higher?

The probability is ________. ​(Round to the nearest thousandth as​ needed.)

c. What is the probability that the Finnish citizen invests in the stock market and has an IQ score of 6 or​ higher?

The probability is ________.. ​(Round to the nearest thousandth as​ needed.)

d. What is the probability that the Finnish citizen invests in the stock market or has an IQ score of 6 or​ higher?

The probability is ________.. ​(Round to the nearest thousandth as​ needed.)

e. What is the probability that the Finnish citizen does not invest in the stock​ market?

The probability is ________.. ​(Round to the nearest thousandth as​ needed.)

f. Are the events​ {Invest in the stock​ market} and​ {IQ score of​ 1} mutually​ exclusive? Choose A,B,C or D

A. ​Yes, they are mutually exclusive because there are no Finnish citizens who invest in the stock market and have an IQ score of 1.

B. ​Yes, they are mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1.

C. ​No, they are not mutually exclusive because the probability that a Finnish citizen invests in the stock market and has an IQ score of 1 is very small.

D. ​No, they are not mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1.

Let Xi be a random variable that takes on the value 1 with probability p and the value 0 with probability q = 1 − p. As we have learnt, this type of random variable is referred to as a Bernoulli trial. This is a special case of a Binomial random variable with n = 1.

a. Show the expected value that E(Xi)=p, and Var(Xi)=pq

b. One of the most common laboratory tests performed on any routine medical examination is a blood count. The two main aspects of a blood count are (1) counting the number of white blood cells (the “white count”) and (2) differentiating the white blood cells that do exist into five categories—namely, neutrophils, lymphocytes, monocytes, eosinophils, and basophils (called the “differential”). Both the white count and the differential are used extensively in making clinical diagnoses. We concentrate here on the differential, particularly on the distribution of the number of neutrophils k out of 100 white blood cells (which is the typical number counted). We will see that the number of neutrophils follows a binomial distribution. In this case, let X1, . . . , Xn indicate the neutrophils status among 100 white blood cells: n = 100 and Xi = 1 if the ith white blood cell is a neutrophil and Xi = 0 if the ith white blood cell is not a neutrophil, where i = 1, . . . , 100. Show the expected value that E(Xi) and Var(Xi).

c. Can we approximate the distribution of X by a normal distribution? Please explain why or why not. If we can, what is the pdf of the normal distribution to use.

You have just been put in charge of safety at your plant. The probability of an injury occuring on any given day is p. Your boss says that once the company has 10 totoal days in which at least one injury is reported the insurance premium triples. To plan financially, she wants to know how many days to expect until the insurance premium is going to triple. Write a class called SafetyAnalysis.java that does the following:

a. Reads in a value of p from the user. Checks if it is a double and a feasible probability.

b. Determines if there is an injury each day. To do this, generate a random number between 0 and 1. If the number you generated is less than p then there was an injury. Otherwise, there was not an injury on that day.

c. Continue determining if there was an injury each day until a total of 10 days worth of injuries have occurred (hint: use a loop where you don’t know how many iterations are required).

d. Repeat b. - c. 1000 times (hint: use a loop where you do know how many iterations are required). Return the average number of days it takes until 10 total injuries occur. (hint: each time you complete c., you have a new value to include in your average) e. Report the average number of days over the 1000 experiments that it takes until 10 days of injuries occur. Print this value to the screen with the appropriate labeling information

In c++, please make it short and simple

A hotel chain needs a program which will produce statistics for the hotels it owns.

Write a program which displays the occupancy rate and other statistics for any of the chain’s large hotels (all are 20 floors with 16 rooms each floor).

In main:

-declare a 20 X 16 array of “int” named hotel to represent a hotel’s 20 floors and 16 rooms per floor.

Then in main, repeatedly:

-call a function which fills the hotel array with 1s and 0s, where 1 indicates an occupied room and 0 indicates an unoccupied room. Call a second function to validate that each entry is either 1 or 0 by having the second function access the original entry using a pointer in its parameter list.

-pass the hotel array to a third function which dynamically allocates a new size 20 “int” array with each element representing a floor of the hotel and the floor’s number of occupied rooms; place the number of occupied rooms of each floor into the new array and return it to main.

-display the floor number** and number of occupied rooms on each floor by incrementing the address of the new array.

-also calculate and display the hotel’s overall occupancy rate to 1 decimal (total rooms occupied per total rooms), and the floor number** and number of occupied rooms of the floor with the highest occupancy.

-process another hotel (unknown number of hotels in chain).

**NOTE: hotels do not have a floor numbered 13 due to guests’ superstitions.

To create your screen print, temporarily set the floors and rooms to 3 and 5 respectively to reduce data entry, and enter:

Floor #1: occupied, occupied, unoccupied, occupied, unoccupied

Floor #2: occupied, unoccupied, occupied, occupied, occupied

Floor #3: occupied, unoccupied, unoccupied, unoccupied, occupied

Consider a computer technical support center where personnel take calls and provide service. The time between calls ranges from 1 to 4 minutes. There are two technical support people – Ayşe and Burak. Ayşe is more experienced and can provide service faster than Burak. System works as follows:

• Ayşe takes the call if both technical support are idle.
• If Ayşe is busy and Burak is idle, Burak takes the call.
• If both Ayşe and Burak are busy, call waits in a queue until one of them gets idle.

Simulate the system for 8 calls. Interarrival distribution of calls and service time distributions for Ayşe and Burak are provided below.

Given that the first arrival occurs at time t = 0, create a record of hand simulation (on the empty table given below) and compute the following performance measures:

1. Average waiting time per customer
2. Average time in system
3. Average service time
4. Average interarrival time
5. Utilization of Ayşe
6. Utilization of Burak
7. Average number of customers in queue
8. Average number of customers in system

In the “when Ayşe becomes available” and “when Burak becomes available” columns you can write the time when Ayşe/Burak becomes available in order to make the simulation easier for you. In the first call, since both servers are idle, Ayşe takes the call.