the mean final examination scores for students taking SM2703 is 30 marks (out f 50 marks) with standard deviation of 6 marks. Assume that the final scores are approximately normal. Two random samples were taken randomly consisting of 32 and 50 students respectively. What is the probability that: a) The mean final examination scores will differ by more than 3 marks? b) Mean final examination scores from group 1 is larger than group 2? vv

Q3.(15) The SAT scores for US high school students are normally distributed with a mean of 1500 and a standard deviation of 100.

1.(5) Calculate the probability that a randomly selected student has a SAT score greater than 1650.

2.(5) Calculate the probability that a randomly selected student has a SAT score between 1400 and 1650, inclusive.

3.(5) If we have random sample of 100 students, find the probability that the mean scores between 1485 and 1510, inclusive.

4. The joint density function of (X, Y ) is f(x,y)=2(x+y), 0≤y≤x≤1

. Find the correlation coefficient ρX,Y .

5. The height of female students in KU follows a normal distribution with mean 165.3 cm and s.d. 7.3cm. The height of male students in KU follows a normal distribution with mean 175.2 cm and s.d. 9.2cm. What is the probability that a random female student is taller than a male student in KU?

Listed below are ten randomly selected IQ scores of statistics students:

111   115   118 100   106   108   110   105   113   109

Using methods for hypothesis testing, you can confirm that these data have the following sample statistics: n = 10,   

109.5, s = 5.2

Using a 0.05 significance level, test the claim that statistics students have a mean IQ score greater than 100, which is the mean IQ score of the general population.

Several students were tested for reaction times​ (in thousandths of a​ second) using their right and left hands.​ (Each value is the elapsed time between the release of a strip of paper and the instant that it is caught by the​ subject.) Results from five of the students are included in the graph to the right. Use a 0.02 significance level to test the claim that there is no difference between the reaction times of the right and left hands.

Right Hand: 124, 118, 149, 183, 199

Left Hand: 144, 148, 174, 215, 225

12. Suppose that the Department of education would like to test the hypothesis that the
average debt load of graduating students with a Bachelor’s degree is equal to
$17,000. A random sample of 34 students had an average debt load of $18,200. It is
believed that the population standard deviation for student debt load is $4,200. The
Department of Education would like to set ? = 0.01.
a. State the null and alternative hypotheses.
b. Calculate the test statistic.
c. Find the critical value(s).
d. What do you conclude? Why?

How come despite spending billions of dollars pharmaceutical companies are not able to find 'the magic bullet' to cure mental disorders?

(Note: your response must focus only on the biological/anatomical/physiological aspects. Any response that is based on social/economic factors will not be accepted. In the past some students focused on expressing views on how evil the pharmaceutical companies are and they deliberately refuse to find the magic bullet because it is not in their economic interest. Those students received score of zero for this RT)

Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of 500 and a standard deviation of 100. Find the probability that a student will score...

a) over 650

b) less than 459

c) between 325 and 675

d) If a school only admits students who score over 680, what proportion of the student's pool would be eligible for admission?

e) what limit (score) would you set that makes the top 20% of the students eligible?

From a random sample of 77 students in an introductory finance class that uses​ group-learning techniques, the mean examination score was found to be 76.9376.93 and the sample standard deviation was 2.52.5. For an independent random sample of 88 students in another introductory finance class that does not use​ group-learning techniques, the sample mean and standard deviation of exam scores were 70.8870.88 and 8.58.5​, respectively. Estimate with 9999​% confidence the difference between the two population mean​ scores; do not assume equal population variances.

A group of students takes a 10 point quiz. You have the scores for each student and decide to calculate the correlation between (a) the number of correct answers on the quiz with (b) the number of incorrect answers on the quiz.

A. What would r equal? If you’re stuck, think about this a bit. If you’re really stuck, it may help to make a scatterplot based 10 students getting various scores on the quiz. _________________ (1 point)

B. How did you arrive at your conclusion? (1 point)