Statistics/probability H/W solution correct answers

Statistics/probability H/W solution correct answers

Instructions: Please show all work, this includes formulas used and writing down what you entered into the calculator in case you use the calculator to solve problems. 

1.        The mean output of an amplifier is 181 watts.  It has σ = 10 watts.  If 98 amplifiers are sampled, what is the probability that the average output is between 178.9 and 183.1 watts?  (6 points)

2.       Suppose that 56% of students at a university are in the College of Business.  A sample of 803 students is taken.  What is the probability that the sample proportion of students in the College of Business is greater than 53%? (6 points)

3.       Given a confidence interval for a population mean of 11.78 < µ < 21.96, determine the original point estimate for the interval and the margin of error.  (6 points)

4.        A chemist would like a margin of error for his experiment on chemical viscosity to be no more than 0.6217.    How large a sample must he use if σ = 0.858 and he would like to have a 95% confidence level?   (6 points)

5.       When must a critical t value be used rather than a critical z value? (4 points)

6.       The average GPA for a sample of 100 high school students considering attending a local university is 3.21 with s = 0.17.  Determine a 99% confidence interval for the population mean.  Interpret the interval. (8 points)

7.       The following is a random sample of the annual salaries of high school counselors in the US.  Assuming that the distribution of salaries is approximately normal, construct a 90% confidence interval for the mean salary of high school counselors across the US.  Interpret the interval.  (8 points)

$51,050

$38,740

$65,360

$42,640

$55,340

$32,980

$49,540

8.       Case studies show that out of 10,351 convicts who escaped from US prisons, only 7867 were recaptured.  Let p represent the proportions of all escaped convicts who will eventually be recaptured.  Find a point estimate for p.  Find a 99% confidence interval for p.  Interpret the interval.  (8 points)

9.        Samples of diameters taken from 11 gaskets off an assembly line are:

9.7, 10.6, 10.3 10.4, 9.9, 9.7, 10.1, 10.1, 10.4, 9.4 and 9.7

 Build a 95% confidence interval for the population standard deviation.  Please refer to the chi-square table.  (8 points)

10.   Frozen Food Company uses a machine that packages blueberries in 7 pound portions.  A sample of 30 packages has a variance of 0.1225 pounds.  Construct a 90% confidence interval for the population variance.  Please refer to the chi –square table.  (8 points)