(A) If 120 scores are chosen from a normal distribution with mean and standard deviation 8 , how many scores x would be expected to satisfy 67 ≤ x ≤ 83 (B) Usea graphing calculator to generate 120 scores from the normal distribution with mean 75 and standard deviation 8 . Determine the number of scores x such that 67 ≤ x ≤ 83 , and compare your results with the answerto part (A).
(A) If 120 scores are chosen from a normal distribution with mean and standard deviation 8 , how many scores x would be expected to satisfy 67 ≤ x ≤ 83 (B) Usea graphing calculator to generate 120 scores from the normal distribution with mean 75 and standard deviation 8 . Determine the number of scores x such that 67 ≤ x ≤ 83 , and compare your results with the answerto part (A).
Solution Summary: The author calculates the number of scores that satisfies 67le xl 83 if 120 scores are chosen from a normal distribution with mean as 75 and standard deviation as
(A) If
120
scores are chosen from a normal distribution with mean and standard deviation
8
, how many scores
x
would be expected to satisfy
67
≤
x
≤
83
(B) Usea graphing calculator to generate
120
scores from the normal distribution with mean
75
and standard deviation
8
. Determine the number of scores
x
such that
67
≤
x
≤
83
, and compare your results with the answerto part (A).
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
2. Consider the ODE
u' = ƒ (u) = u² + r
where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r:
(a) Sketch ƒ(u) = u² + r and determine the equilibrium points.
(b) Draw the phase line.
(d) Determine the stability of the equilibrium points.
(d) Plot the direction field and some sample solutions,i.e., u(t)
(e) Describe how location of the equilibrium points and their stability change as you increase the
parameter r.
(f) Using the matlab program phaseline.m generate a solution for each value of r and the initial
condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption.
(g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode
over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to
turn in a plot for (g), just describe what happens.
The following are suggested designs for group sequential studies. Using PROCSEQDESIGN, provide the following for the design O’Brien Fleming and Pocock.• The critical boundary values for each analysis of the data• The expected sample sizes at each interim analysisAssume the standardized Z score method for calculating boundaries.Investigators are evaluating the success rate of a novel drug for treating a certain type ofbacterial wound infection. Since no existing treatment exists, they have planned a one-armstudy. They wish to test whether the success rate of the drug is better than 50%, whichthey have defined as the null success rate. Preliminary testing has estimated the successrate of the drug at 55%. The investigators are eager to get the drug into production andwould like to plan for 9 interim analyses (10 analyzes in total) of the data. Assume thesignificance level is 5% and power is 90%.Besides, draw a combined boundary plot (OBF, POC, and HP)
4. Solve the system of equations and express your solution using vectors.
2x1 +5x2+x3 + 3x4 = 9
-x2+x3 + x4 = 1
-x1-6x2+3x3 + 2x4
= -1
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