1. An African hospital is treating patients who have Lhassa Fever. Forty percent (0.40) of patients with this disease survive and each patient lives or dies independently of other patients. Answer the following:
a. There are currently 7 Lhassa Fever patients in the hospital. Use binomial calculations (Table C attached) to determine the exact probability that at least 6 survive. (6 points)b. Over the next six months the hospital expects 50 patients with Lhassa Fever. Approximate the probability that more than 70% of these patients die. (6 points)
c. How do you know whether your approximation in part b will work well or not?2. In a study of plant safety, it was found that the time it took for machine operators to react to a warning light was normally distributed with mean 1 second and standard deviation 0.3 second. Ten (10) operators are independently tested for their reaction times. What is the probability that the average reaction time of these 10 exceeds 1.2 seconds? (8 points)
(5 points)
3. Define the following events A = student is a business major and B = student owns a computer. Suppose it is known that at UAF the probability that a randomly selected student is a business major is P(A) = 0.35, and similarly P(B) = 0.40, and P(A and B) = 0.10 Determine the following (5 points each):
a. P(A or B)b. Find the probability that a randomly selected student is a business major given that they own a computer.
c. Are the events A and B independent? Circle Yes or NoExplanation:
d. Find P(A|Bc)
4. Suppose you decide to enter a local lottery. You spend $5 for
a lottery ticket. If you win the drawing, you will receive a prize
worth $1005. Only 500 tickets are sold for the lottery and the winner
is to be selected by a random drawing of one ticket. What is your
expected (average) gain or loss. (6 points)
5. True or False (Circle one) The standard deviation of the difference of two random variables is the sum of the standard deviations of the two variables. (4 points)
6. Many opinion surveys ask the respondent their reaction to a statement
like "the legislature should use the Alaska Permanent Fund for this years
budget". The respondent is asked to circle one of the possible responses
(1) Strongly agree (2) Agree (3) Neutral (4) Disagree
and (5) Strongly disagree. The random variable X records which answer
a respondent gives to the question. So the possible values of X are
1, 2, 3, 4, and 5. Answer the following:
a. The random variable X is a (record the letter of the correct statement in the answer space)(4 points) Answer ______i) discrete random variable that is not binomial
b. Suppose you are told the distribution of X is
| X | 1 | 2 | 3 | 4 | 5 |
| P(X) | -0.2 | 0.4 | 0.3 | 0.2 | 0.3 |
7. You want to compute a 98% confidence interval for a population mean.
Assume that the population variance is 100. What sample size is required
so that the margin of error in estimating the mean is 3. (6 points)
8. Give three (3) factors that influence the width of a confidence interval
for the population mean.
(6 points)
9. Suppose that cellulose content of hay is normally distributed with standard deviation 10 mg/g. A sample of 25 plots of hay yielded a mean content of = 145 mg/g. You want to test H0: µ = 140 versus Ha: µ > 140
a. Calculate the value of the test statistic for this problem. (6 points)10. Suppose you observe a value of z = 1.83 when testing H0: µ = 12 versus Ha: µ not = 12. Determine the P-value of your test. (5 points)b. Describe in terms of this problem what a type II error would be. (5 points)
c. For the purpose of conducting this hypothesis test, is it important that the cellulose content of hay is normally distributed? Why or why not? (5 points)