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Condition |
free/or 0.5$ |
| m389 | Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows: |
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| m390 | Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows:
Shock resistance
High Low
Scratch high 70 9
Resistance low 16 5
Let A denote the event that a disk has high shock resistance, and let B denote the event that a disk has high scratch resistance. Are events A and B independent? |
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| m391 | Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows:
Shock resistance
High Low
Scratch high 70 9
Resistance low 16 5
Let A denote the event that a disk has high shock resistance, and let B denote the event that a disk has high scratch resistance.
If a disk is selected at random, determine the following probabilities:
(a) P (A) (b) P (A)
(c) P (A`) (d) P (A ∩ B)
(e) (A U B) (f) (A` U B) |
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| m392 | Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows:
Shock resistance
High Low
Scratch high 70 9
Resistance low 16 5
(a) If a disk is selected at random, what is the probability that its scratch resistance is high and its shock resistance is high?
(b) If a disk is selected at random, what is the probability that its scratch resistance is high or its shock resistance is high?
(c) Consider the event that a disk has high scratch resistance and the event that a disk has high shock resistance. Are these two events mutually exclusive? |
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| m393 | Do husbands and wives like the same TV shows? A recent study by Nielsen Media Research asked a young married couple to rank 14 shows from best to worst. A rank of 1 indicates the best-liked show and a rank of 14 the least-liked show. The results for one married couple follow.
a. Draw a scatter diagram. Place the male rankings on the horizontal axis and the female rankings on the vertical axis.
b. Compute the coefficient of rank correlation between the male and female rankings.
c. At the .05 significance level, is it reasonable to conclude there is a positive association between the tworankings? |
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| m394 | Dole Pineapple Inc. is concerned that the 16-ounce can of sliced pineapple is being over-filled. Assume the standard deviation of the process is .03 ounce. The quality-control department took a random sample of 50 cans and found that the arithmetic mean weight was 16.05 ounces. At the 5% level of significance, can we conclude that the mean weight is greater than 16 ounces? Determine the p-value. |
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| m395 | Dottie’s Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 7% of the returns she prepared last year.
Assuming this rate continues into this year and she prepares 80 returns, what is the probability that she makes errors on:
a. More than six returns?
b. At least six returns?
c. Exactly six returns? |
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| m396 | Dr. Richmond, a psychologist, is studying the daytime television viewing habits of college students. She believes 45% of college students watch soap operas during the afternoon. To further investigate, she selects a sample of 10.
a. Develop a probability distribution for the number of students in the sample who watch soap operas.
b. Find the mean and the standard deviation of this distribution.
c. What is the probability of finding exactly four students who watch soap operas?
d. What is the probability less than half of the students selected watch soap operas? |
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| m397 | Dr. Stallter has been teaching basic statistics for many years. She knows that 80% of the students will complete the assigned problems. She has also determined that among those who do their assignments, 90% will pass the course. Among those students who do not do their homework, 60% will pass. Mike Fishbaugh took statistics last semester from Dr. Stallter and received a passing grade. What is the probability that he completed the assignments? |
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| m398 | Drs. Trythall and Kerns are studying the mobility of executives in selected industries. Their research measures mobility using a score based on the number of times an executive has moved, changed companies, or changed jobs within a company over the last 10 years. The highest number of points is awarded for moving and changing companies; the fewest, for changing jobs within a company and not moving. They randomly sampled five executives in the chemical industry, six in the retail industry, five in the Internet industry, and five in the aerospace industry. The distribution of scores does not follow the normal probability distribution. Develop an appropriate test to determine if there is a difference in the mobility scores in the four industries. Use the .05 significancelevel. |
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| m399 | During a national debate on changes to health care, a cable news service performs an opinion poll of 500 small-business owners. It shows that 65% of small-business owners do not approve of the changes. Develop a 95% confidence interval for the proportion opposing health care changes. Comment on the result. |
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| m400 | During recent seasons, Major League Baseball has been criticized for the length of the games. A report indicated that the average game lasts 3 hours and 30 minutes. A sample of 17 games revealed the following times to completion.
Can we conclude that the mean time for a game is less than 3.50 hours? Use the .05 significancelevel. |
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| m401 | During the 1990s, the fatality rate for lung cancer was 80 per 100,000 people. After the turn of the century and the establishment of newer treatments and adjustment in public health advertising, a random sample of 10,000 people exhibits only six deaths due to lung cancer. Test at the .05 significance level whether that data are proof of a reduced fatality rate for lung cancer. |
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| m402 | During the process of producing toilet paper, Scott Paper randomly selects a toilet paper roll 5 times throughout the day and subjects each roll to a stress test to see how often the paper tears. Over a 3-day period, the testing of 15 rolls found the following number of defectives in each roll: 2, 3, 1, 2, 2, 1, 3, 2, 2, 1, 2, 2, 1, 0, and 0. Construct a control chart for the process and comment on whether the process is “in control.” |
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| m403 | Dylan Jones kept careful records of the fuel efficiency of his new car. After the first nine times he filled up the tank, he found the mean was 23.4 miles per gallon (mpg) with a sample standard deviation of 0.9 mpg.
a. Compute the 95% confidence interval for his mpg.
b. How many times should he fill his gas tank to obtain a margin of error below 0.1 mpg? |
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| 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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