Reliability of a manufacturing network. A team of industrial management university professors investigated the reliability of a manufacturing system that involves multiple production lines (Journal of Systems Sciences & Systems Engineering, March 2013). An example of such a network is a system for producing integrated circuit (IC) cards with two production lines set up in sequence. Items (IC cards) first pass through Line 1 , then are processed by Line 2. The probability distribution of the maximum capacity level $(x)$ of each line is shown below. Assume the lines operate independently. Find the mean maximum capacity for each line. Interpret the results practically.

Line	Maximum Capacity, $x$	$p(x)$
1	0	$.01$
	12	$.02$
	24	$.02$
36	$.95$
2	0	$.002$
	35	$.002$
	70	$.996$

Personnel dexterity tests. Personnel tests are designed to test a job applicant's cognitive and/or physical abilities. The Wonderlic IQ test is an example of the former; the Purdue Pegboard speed test involving the arrangement of pegs on a peg board is an example of the latter. A particular dexterity test is administered nationwide by a private testing service. It is known that for all tests administered last year, the distribution of scores was approximately normal with mean 75 and standard deviation $7.5$. The testing service reported to a particular employer that one of its job candidate's scores fell at the 98th percentile of the distribution (i.e., approximately $98 \%$ of the scores were lower than the candidate's, and only $2 \%$ were higher). What was the candidate's score?

Consider the probability distribution shown here. Use your intuition to find the mean for each distribution. How did you arrive at your choice?

$$\begin{aligned} &\begin{array}{llll} \hline x & 0 & 1 & 2 \\ p(x) & .3 & .4 & .3 \\ \hline \end{array}\\ &\begin{array}{llll} \hline y & 0 & 1 & 2 \\ p(y) & .1 & .8 & .1 \\ \hline \end{array} \end{aligned}$$

A die is tossed. Let $x$ be the number of spots observed on the upturned face of the die. Display the probability distribution of $x$ in graphical form.

Give an example of a continuous random variable that would be of interest to a stockbroker.

The Journal of Business & Economic Statistics (July 2000) presented a case in which a charge of gender discrimination was filed against the U.S. Postal Service. At the time, there were 302 U.S. Postal Service employees (229 men and 73 women) who applied for promotion. Of the 72 employees who were awarded promotion, 5 were female. Make an inference about whether or not females at the U.S. Postal Service were promoted fairly.

Refer to the Journal of Systems Sciences & Systems Engineering (Mar. 2013) study of the reliability of a manufacturing system that involves multiple production lines. Consider, again, the network for producing integrated circuit (IC) cards with two production lines set up in sequence. a. Find the mean maximum capacity for each line. Interpret the results practically. b. Find the standard deviation of the maximum capacity for each line. Interpret the results practically.

A tea.in of industrial management university professors investigated the reliability of a manufacturing system that involves multiple production lines (Journal of Systems Sciences & Systems Engineering, Mar. 2013). An example of such a network is a system for producing integrated circuit (IC) cards with two production lines set up in sequence. Items (IC cards) first pass through Line 1 and then are processed by Line 2. Toe probability distribution of the maximum capacity level of each line is shown in the next column. Assume the lines operate independently.

$$\begin{matrix} \text{Line} & \text{Maximum Capacity, x} & \text{p(x)}\\ \text{1} & \text{0} & \text{.01}\\ \text{1} & \text{12} & \text{.02}\\ \text{1} & \text{24} & \text{.02}\\ \text{1} & \text{36} & \text{.95}\\ \text{2} & \text{0} & \text{.002}\\ \text{2} & \text{35} & \text{.002}\\ \text{2} & \text{70} & \text{.996}\\ \end{matrix}$$

Find the probability that the maximum capacity level for Line 2 will exceed 30 items.

A literature professor decides to give a 20-question true–false quiz to determine who has read an assigned novel. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less than .05. What score should she set as the lowest passing grade?

The British Columbia Institute of Technology provides on its Web site ( www.math.bcit.ca ) practical applications of statistics to mechanical engineering. The following is a Poisson application. A roll of plasticcoated wire has an average of .8 flaws per 4-meter length of wire. Suppose a quality control engineer will sample a 4-meter length of wire from a roll of wire 220 meters in length. If no flaws are found in the sample, the engineer will accept the entire roll of wire. What is the probability that the roll will be rejected? What assumption did you make to find this probability?

The British Columbia Institute of Technology provides on its website (www.math. bcit.ca) practical applications of statistics to mechanical engineering. The following is a Poisson application. A roll of plastic-coated wire has an average of .8 flaws per 4-meter length of wire. Suppose a quality control engineer will sample a 4-meter length of wire from a roll of wire 220 meters in length. If no flaws are found in the sample, the engineer will accept the entire roll of wire. What is the probability that the roll will be rejected? What assumption did you make to find this probability?

Reliability of a manufacturing network. Refer to the Journal of Systems Sciences & Systems Engineering (March 2013) study of the reliability of a manufacturing system for producing integrated circuit (IC) cards that involves two production lines. Recall that items (IC cards) first pass through Line 1, then are processed by Line 2 . The probability distribution of the maximum capacity level of each line is reproduced below. Consider an IC card randomly selected at some point in the production process. Let $X$ represent the line number and $Y$ represent the maximum capacity of the line at the time of selection. Assuming the lines operate independently, find the bivariate probability distribution $p(x, y)$.

$$\begin{array}{ccc} \hline \text { Line, } X & \text { Maximum Capacity, } Y & p(y) \\ 1 & 0 & .01 \\ & 12 & .02 \\ & 24 & .02 \\ & 36 & .95 \\ \hline 2 & 0 & .002 \\ & 35 & .002 \\ & 70 & .996 \\ \hline \end{array}$$

A professor finds that the grades in a large class are normally distributed. The mean of the grades is 64, and the standard deviation is 10. If the professor decides to give an A grade to the students in the top 9% of the class, what is the cut-off score for an A?

TRUE or FALSE

A minimum wage above $10 per hour is not a binding minimum wage in this market. (economists call a minimum wage that prevents the labor market from reaching equilibrium a binding minimum wage.)