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# Probability , Confidence Interval

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1. Suppose that A and B are independent events such that P (A bar) = 0.50 and P (B) = 0.70. Find P ( A intersection B) and P (AUB) .

2. Let A and B be two events such that P(A)= 0.20 and P(B) = 0.05. .
(a) Determine P (AUB) , given that A and B are mutually exclusive .
(b) Determine P (AUB) , given that A and B are independent .
3. At a certain college, 47 % of the students are female, and 19 % of the students major in finance. Furthermore, 8 % of the students both are female and major in finance.

(a) What is the probability that a randomly selected finance major is female? Round your answer to 2 decimal places.

(b) What is the probability that a randomly selected female student majors in finance? Round your answer to 2 decimal places.

4. Suppose that a certain college class contains 47 students. Of these, 29 are freshmen, 28 are mathematics majors, and 11 are neither. A student is selected at random from the class.
(a) What is the probability that the student is both a freshman and a mathematics major?
(b) Given that the student selected is a mathematics major, what is the probability that she is also a freshman?

5. For each of the variables described below, indicate whether the variable is a quantitative or a categorical (qualitative) variable. Also, indicate the level of measurement for the variable: nominal, ordinal, interval, or ratio. Make sure your responses are the most specific possible.

Variables
(a) End-of year stock, classification (high yield, medium yield, or low yield)
(b) Temperature (in degrees Celsius)
(c) Total elapsed time (in seconds) for computation of an assembly line operation
(d) Native Language

6. The standard deviation of test scores on a certain achievement test is 11.3. A random sample of 60 scores on this test had a mean of 74.3. Based on this sample, find a 99% confidence interval for the true mean of all scores. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place
(a) What is the lower limit of the 99% confidence interval?
(b) What is the upper limit of the 99% confidence interval?

7. A certain brokerage house wants to estimate the mean daily return on a certain stock. A random sample of 10 days yields the following return percentages:
2.26, -0.39, 1.56, -2.73, 0.4, -1.56, 0.99, 2.05, -2.57, -2.12
If we assume that the returns are normally distributed, find a 90% confidence interval for the mean daily return on this stock. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place
(a) What is the lower limit of the confidence interval?
(b) What is the upper limit of the confidence interval?

8. The workers' union at a particular university is quite strong. About 96% of all workers employed by the university belong to the workers' union. Recently, the workers went on strike, and now a local TV station plans to interview 4 workers (chosen at random) at the university to get their opinions on the strike. What is the probability that exactly 2 of the workers interviewed are union members?
Round your response to at least three decimal places.

9. Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than 50 parts per million (ppm). PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of 47.8 ppm and a standard deviation of 8 ppm. The Environmental Protection Agency takes a random sample of 38 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 49.5 ppm or more. Find the probability that the disposal of such capacitors will be regulated.
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.