The reading speed of second grade students in a large city is approximately​ normal, with a mean of

92 words per minute​ (wpm) and a standard deviation of 10 wpm.

​(a) What is the probability a randomly selected student in the city will read more than 97 words per​ minute?

Interpret this probability.

(b) What is the probability that a random sample of 12 second grade students from the city results in a mean reading rate of more than 97 words per​ minute?

Interpret this probability.

(c) What is the probability that a random sample of 24 second grade students from the city results in a mean reading rate of more than 97 words per​ minute?

Interpret this probability.

(d) What effect does increasing the sample size have on the​ probability? Provide an explanation for this result.

(e) A teacher instituted a new reading program at school. After 10 weeks in the​ program, it was found that the mean reading speed of a random sample of 21 second grade students was 94.3 wpm. What might you conclude based on this​ result?

(f) There is a​ 5% chance that the mean reading speed of a random sample of 25 second grade students will exceed what​ value?

More than 100 million people around the world are not getting enough sleep; the average adult needs between 7.5 and 8 hours of sleep per night. College students are particularly at risk of not getting enough shut-eye.

A recent survey of several thousand college students indicated that the total hours of sleep time per night, denoted by the random variable X, can be approximated by a normal model with E(X) = 6.9 hours and SD(X) = 1.27 hours.

Question 1. Find the probability that the hours of sleep per night for a random sample of 4 college students has a mean xbetween 6.84 and 6.97.

(use 4 decimal places in your answer)

Question 2. Find the probability that the hours of sleep per night for a random sample of 16 college students has a mean xbetween 6.84 and 6.97.

(use 4 decimal places in your answer)

Question 3. Find the probability that the hours of sleep per night for a random sample of 25 college students has a mean xbetween 6.84 and 6.97.

(use 4 decimal places in your answer)

Question 4. The Central Limit Theorem was needed to answer questions 1, 2, and 3 above.

TrueFalse

QUESTION 1 [10] It is known that 80 % of all students have their own laptops, thus in a random sample of eight students, find the following probabilities: 1.1) That exactly seven students will have their own laptops. (3) 1.2) That at least six students will have their own laptops. (4) 1.3) That at most five students will have their own laptops (4) QUESTION 2 [11] The number of accidents that occur on an assembly line have a Poisson distribution with an average of five accidents per week. 2.1) Find the probability that exactly two accidents will occur in a week. (3) 2.2) Find the probability that a particular week will be accident free. (3) 2.3) Find the probability that at least three accidents will occur in a week. (3) 2.4) If the accidents in different weeks are independent of each other, find the expected number of accidents to occur in a year. (2) QUESTION 3 [9] The time it takes a student to complete an assignment is normally distributed with mean 45 minutes and a standard deviation of 7 minutes. Find the probability that it takes the following lengths of time for a student to complete an assignment. 3.1) Between 45 and 56 minutes. (3) 3.2) Less than 33 minutes (3) 3.3) More than 29 minutes (3)

A) The total distances covered by GIMPA Undergraduate students to and from their work places every month is normally distributed with a mean 105 km and variance of 225 km2. a. What percentage of the population of students covered less than 90 km in a month in other words what is the probability of finding a student who covers less than 90 km in a month? (1 mark) b. The percentage of students who cover above 140 km every month (1 mark) c. The percentage of students who cover between 100 and 120 km every month (1 mark) d. What is the least distance of the top 0.1 decile category of the distances covered by students in a month? (2 mark) B) A health clinic found that in a sample of 200 women, the mean and the standard deviation of their masses are 85.5kg and 10.5kg, respectively. Also, 115 women were found to be over-weight. a. Find point estimates of the mean mass and proportion of over-weight in women population. (1 mark) b. Construct a 95% confidence interval for population mean mass. ( 2 marks) c. Construct a 95% confidence for proportion of over-weight in women population. (2marks)

1. survey of the MBA students at a university in the United States classified the country of origin of the students as seen in the table.

1. What percent of all MBA students were from North America?

2. What percent of the Two-year MBA students were from North America?

3. What percent of the evening MBA students were from North America?

4. What is the marginal distribution of origin?

1. Using the table below, calculate the variance of X, variance of Y, standard deviation of X, standard deviation of Y, the covariance between X and Y, the correlation coefficient between X and Y, and find the regression line assuming X is the independent variable (find the slope and the intercept). Show your work.

To better understand the financial burden students are faced with each term, the statistics department would like to know how much their ST201 students are spending on school materials on average. Let’s use our class data to calculate a 95% confidence interval to estimate the average amount ST201 students spend on materials each term.

The average from our student survey is $248 and the number of students sampled is 90.

Assume ? = $220.
State the question of interest.

On average, how much do ST201 students spend on school materials each term?

1. (1 point) Identify the parameter.

2. Check the conditions.

a. (2 points) Does the data come from a random sample? What are some potential biases about the way the data was collected?

b. (1 point) Is the sample size large enough for distribution of the sample mean to be normal according to the rules for Central Limit Theorem?

c. (3 points) Set up and calculate the confidence interval. Show work! ∗σ

Our estimate, x̅ = _______ z critical value = _______ Standard error, √n = __________

d. (3 points) Return to the question of interest and describe your results in this setting. Be sure to include level of confidence used, your point and interval estimates and context!

A) 100 random college students were asked abouttheir breakfast beveragepreferences. 48drink coffee. 28drink orange juice.24drink apple juice. 18 drink orange juice and coffee. 15 drink apple juiceand coffee. 8drink apple and orange juice. 5 drink all three. How many did not drink a beverage?

B) 100 random college students were asked about their breakfast beverage preferences. 48 drink coffee. 28 drink orange juice. 24 drink apple juice. 18 drink orange juice and coffee. 15 drink apple juice and coffee. 8 drink apple and orange juice. 5 drink all three. How many students drink coffee, but not apple juice?

C) 100 random college students were asked about their breakfast beverage preferences. 48 drink coffee. 28 drink orange juice. 24 drink apple juice. 18 drink orange juice and coffee. 15 drink apple juice and coffee. 8 drink apple and orange juice. 5 drink all three. How many students drink coffee, but not orange juice?

Aldrich Ames is a convicted traitor who leaked American secrets to a foreign power. Yet Ames took routine lie detector tests and each time passed them. How can this be done? Recognizing control questions, employing unusual breathing patterns, biting one's tongue at the right time, pressing one's toes hard to the floor, and counting backwards by 7 are countermeasures that are difficult to detect but can change the results of a polygraph examination†. In fact, it is reported in Professor Ford's book that after only 20 minutes of instruction by "Buzz" Fay (a prison inmate), 85% of those trained were able to pass the polygraph examination even when guilty of a crime. Suppose that a random sample of eleven students (in a psychology laboratory) are told a "secret" and then given instructions on how to pass the polygraph examination without revealing their knowledge of the secret. What are the following probabilities? (Round your answers to three decimal places.)

(a) all the students are able to pass the polygraph examination

(b) more than half the students are able to pass the polygraph examination

(c) no more than half of the students are able to pass the polygraph examination

(d) all the students fail the polygraph examination

Please write a java program that has the following methods in it: (preferably in order)  

1. a method to read in the name of a University and pass it back
2. a method to read in the number of students enrolled and pass it back
3. a method to calculate the tuition as 20000 times the number of students and pass it back
4. a method print the name of the University, the number of students enrolled, and the total tuition

Design Notes:

• The method described in Item #1 above will read in a string and pass it back to the main program. Nothing is passed to the method, but the University name is passed back
  
• The method described in Item #2 above will read in an integer for the number of students enrolled and pass it back to the main program. Nothing is passed to the method, but the University name is passed back to the main program
  
• The method described in Item #3 above will receive the number of students. It will then do the calculation for the tuition and pass back that value, which is a double value to the main program
  
• The method described in Item #4 above will receive all data for printing and pass nothing back to the main program
  

Please copy the java code along with a screen print (snippet) of the final output. I would like both to review the work that I already have done. Thanks in advance!

1. Write the header and the implementation files (.h and .cpp separately) for a class called Course, and a simple program to test it (C++), according to the following specifications:                   

1. Your class has 3 member data: an integer pointer that will be used to create a dynamic variable to represent the number of students, an integer pointer that will be used to create a dynamic array representing students’ ids, and a double pointer that will be used to create a dynamic array to represent the GPAs of each student.

2. Your class has the following member functions:

1. a constructor with an int parameter representing the number of students; the constructor creates the dynamic variable and sets it to the int parameter, creates the two dynamic arrays and sets everything to zero.

2. a function which reads in all the ids and the GPAs into the appropriate arrays.

3. a function called print_info which, for each student, does all of the

                following:

                It prints the student’s id and GPA. If the student’s GPA is greater than or equal to 3.8, it prints “an honor student”.

4. a destructor (hint: delete array)
5. create 5 random instances of Course objects to represents 5 sessons of CSC211, each session includes 20 students, assign random score to each student, calculate the average GPA of all 100 students.