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free/or 0.5$ |
| m404 | An e-mail message can travel through one of two server routes. The probability of transmission error in each of the servers and the proportion of messages that travel each route are shown in the following table. Assume that the servers are independent.
Probability of error
Percentage Of messages server 1 server 2 server 3
server 4
Route 1 30 0.01 0.015
Route 2 70 0.02
0.003 (a) What is the probability that a message will arrive without error?
(b) If a message arrives in error, what is the probability it was sent through route 1? |
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| m405 | Each main bearing cap in an engine contains four bolts. The bolts are selected at random, without replacement, from a parts bin that contains 30 bolts from one supplier and 70 bolts from another.
(a) What is the probability that a main bearing cap contains all bolts from the same supplier?
(b) What is the probability that exactly three bolts are from the same supplier? |
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| m406 | Each month the National Association of Purchasing Managers surveys purchasing managers and publishes the NAPM index. One of the questions asked on the survey is: Do you think the economy is contracting? Last month, of the 300 responding managers, 160 answered yes to the question. This month, 170 of the 290 managers indicated they felt the economy was contracting. At the .05 significance level, can we conclude that a larger proportion of the purchasing managers believe the economy is contracting this month? |
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| m407 | Each of four transmitted bits is classified as either in error or not in error. |
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| m408 | Each of the digits in a raffle is thought to have the same chance of occurrence. The table shows the frequency of each digit for consecutive drawings in a California lottery. Perform the chi-square test to see if you reject the hypothesis at the .05 significance level that the digits are from a uniformpopulation. |
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| m409 | Each of the possible five outcomes of a random experiment is equally likely. The sample space is {a, b, c, d, e}.
Let A denote the event {a, b}, and let B denote the event {c, d, e}. Determine the following:
(a) P (A) (b) P (B)
(c) P (A’) (d) P (A U B)
(e) P (A ∩ B) |
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| m410 | Each of three machined parts is classified as either above or below the target specification for the part. |
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| m411 | Each salesperson at Puchett, Sheets, and Hogan Insurance Agency is rated either below average, average, or above average with respect to sales ability. Each salesperson is also rated with respect to his or her potential for advancement—either fair, good, or excellent. These traits for the 500 salespeople were cross-classified into the following table.
.:.
a. What is this table called?
b. What is the probability a salesperson selected at random will have above average sales ability and excellent potential for advancement?
c. Construct a tree diagram showing all the probabilities, conditional probabilities, and joint probabilities. |
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| m412 | Early in the basketball season, 12 college teams appeared to be outstanding. A panel of sportswriters and a panel of college basketball coaches were asked to rank the 12 teams. Their composite rankings were as follows.
Determine the correlation between the rankings of the coaches and the sportswriters. At the .05 significance level, can we conclude there is a positive correlation between therankings? |
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| m413 | Early Morning Delivery Service guarantees delivery of small packages by 10:30 a.m. Of course, some of the packages are not delivered by 10:30 a.m. For a sample of 200 packages delivered each of the last 15 working days, the following numbers of packages were delivered after the deadline: 9, 14, 2, 13, 9, 5, 9, 3, 4, 3, 4, 3, 3, 8, and 4.
a. Determine the mean proportion of packages delivered after 10:30 a.m.
b. Determine the control limits for the proportion of packages delivered after 10:30 a.m. Were any of the sampled days out of control?
c. If 10 packages out of 200 in the sample were delivered after 10:30 a.m. today, is this sample within the control limits? |
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| m414 | Ecommerce.com, a large Internet retailer, is studying the lead time (elapsed time between when an order is placed and when it is filled) for a sample of recent orders. The lead times are reported in days.
Lead Time (days) Frequency
0 up to 5........... 6
5 up to 10.......... 7
10 up to 15.......... 12
15 up to 20........... 8
20 up to 25........... 7
Total............. 40
a. How many orders were studied?
b. What is the midpoint of the first class?
c. What are the coordinates of the first class for a frequency polygon?
d. Draw a histogram.
e. Draw a frequency polygon.
f. Interpret the lead times using the two charts. |
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| m415 | Eight cavities in an injection-molding tool produce plastic connectors that fall into a common stream. A sample is chosen every several minutes. Assume that the samples are independent.
(a) What is the probability that five successive samples were all produced in cavity one of the mold?
(b) What is the probability that five successive samples were all produced in the same cavity of the mold?
(c) What is the probability that four out of five successive samples were produced in cavity one of the mold? |
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| m416 | An electronic product contains 40 integrated circuits. The probability that any integrated circuit is defective is 0.01, and the integrated circuits are independent. The product operates only if there are no defective integrated circuits. What is the probability that the product operates? |
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| m417 | An electronic scale that displays weights to the nearest pound is used to weigh packages. The display shows only five digits. Any weight greater than the display can indicate is shown as 99999. The random variable is the displayed weight. |
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| m418 | An electronic scale in an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.001 and each fill is independent.
(a) What is the mean number of fills before the line is stopped?
(b) What is the standard deviation of the number of fills before the line is stopped? |
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| m419 | Emily Smith decides to buy a fuel-efficient used car. Here are several vehicles she is considering, with the estimated cost to purchase and the age of the vehicle.
a. Plot these data on a scatter diagram with estimated cost as the dependent variable.
b. Find the correlation coefficient.
c. A regression analysis was performed and the resulting regression equation is Estimated Cost 5 18358 2 1534 Age. Interpret the meaning of the slope.
d. Estimate the cost of a five-year-old car.
e. Here is a portion of the regression software output. What does it tell you?
f. Using the .10 significance level, test the significance of the slope. Interpret the result. Is there a significant relationship between the twovariables? |
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| m420 | An encryption-decryption system consists of three elements: encode, transmit, and decode. A faulty encode occurs in 0.5% of the messages processed, transmission errors occur in 1% of the messages, and a decode error occurs in 0.1% of the messages. Assume the errors are independent.
(a) What is the probability of a completely defect-free message?
(b) What is the probability of a message that has either an encode or a decode error? |
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| m421 | Eric’s Cookie House sells chocolate chip cookies in shopping malls. Of concern is the number of chocolate chips in each cookie. Eric, the owner and president, would like to establish a control chart for the number of chocolate chips per cookie. He selects a sample of 15 cookies from today’s production and counts the number of chocolate chips in each. The results are as follows: 6, 8, 20, 12, 20, 19, 11, 23, 12, 14, 15, 16, 12, 13, and 12.
a. Determine the centerline and the control limits.
b. Develop a control chart and plot the number of chocolate chips per cookie.
c. Interpret the chart. Does it appear that the number of chocolate chips is out of control in any of the cookies sampled? |
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| m422 | Errors in an experimental transmission channel are found when the transmission is checked by a certifier that detects missing pulses. The number of errors found in an eight bit byte is a random variable with the following distribution: |
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| m423 | Estimate the mean and the standard deviation of the following frequency distribution.
Class Frequency
20 up to 30...... 7
30 up to 40...... 12
40 up to 50...... 21
50 up to 60...... 18
60 up to 70...... 12 |
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