Question 411392:
Approximately 16% of the calls to an airline reservation phone line result in a reservation being made.
(a) Suppose that an operator handles 15 calls. What is the probability that none of the 15 calls result in a reservation? (Give the answer to 3 decimals places.)
(b) What assumption did you make to calculate the probability in Part (a)?
Calls are independent Calls are dependent
(c) What is the probability that at least one call results in a reservation being made? (Give the answer to 3 decimals places.)
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2. –/2 points Notes Question: PeckDevStat6 6.E.008.
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In a small city, approximately 47% of those eligible are called for jury duty in any one calendar year. People are selected for jury duty at random from those eligible, and the same individual cannot be called more than once in the same year.
(a) What is the probability that a particular eligible person in this city is selected two years in a row?
(b) What is the probability that a particular eligible person in this city is selected three years in a row?
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3. –/3 points Notes Question: PeckDevStat6 6.E.015.
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Is ultrasound a reliable method for determining the gender of an unborn baby? There is accompanying data on 1000 births in the table below.
Ultrasound
Predicted
Female Ultrasound
Predicted
Male
Actual Gender Is
Female 439 47
Actual Gender Is
Male 132 382
(a) Use the given information to estimate the probability that a newborn baby is female, given that the ultrasound predicted the baby would be female. (Give the answer to three decimal places.)
(b) Use the given information to estimate the probability that a newborn baby is male, given that the ultrasound predicted the baby would be male. (Give the answer to three decimal places.)
(c) Based on your answers to Parts (a) and (b), do you think ultrasound is equally reliable for predicting gender for boys and for girls?
Ultrasound appears to be more reliable in predicting boys Ultrasound appears to be more reliable in predicting girls Ultrasound is equally reliable in predicting boys and girls
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4. –/4 points Notes Question: PeckDevStat6 6.E.019.
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The Los Angeles Times reported that the U.S. Postal Service is getting speedier, with higher overnight on-time delivery rates than in the past. The Price Waterhouse accounting firm conducted an independent audit by seeding the mail with letters and recording ontime delivery rates for these letters. Suppose that the results were as follows (these numbers are fictitious but are compatible with summary values given in the article). Use the given information to estimate some probabilities.
Number of Letters Mailed Number of Letters Arriving on Time
Los Angeles 500 430
New York 500 415
Washington, D.C. 500 400
Nationwide 7000 6020
(a) the probability of an on-time delivery in Los Angeles
(b) the probability of late delivery in Washington, D.C
(c) the probability that two letters mailed in New York are both delivered on time
(d) the probability of on-time delivery nationwide
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5. –/4 points Notes Question: PeckDevStat6 6.E.021.
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The table describes (approximately) the distribution of students by gender and college at a mid-sized public university in the West. We randomly select one student from this university.
College
Gender Education Engineering Liberal arts Science and Math Agriculture Business Architecture
Male 100 2600 2500 1100 2100 2200 300
Female 200 600 1500 1100 900 2200 400
(a) What is the probability that the selected student is a male? (Give the answer to three decimal places.)
(b) What is the probability that the selected student is in the College of Agriculture? (Give the answer to three decimal places.)
(c) What is the probability that the selected student is a male in the College of Agriculture? (Give the answer to three decimal places.)
(d) What is the probability that the selected student is a male who is not from Agriculture? (Give the answer to three decimal places.)
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6. –/3 points Notes Question: PeckDevStat6 6.E.031.
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A radio station that plays classical music has a "by request" program each Saturday evening. The percentages of requests for composers on a particular night are as follows.
Bach 16%
Beethoven 15%
Brahms 7%
Dvorak 4%
Mendelssohn 11%
Mozart 13%
Schubert 10%
Schumann 9%
Tchaikovsky 4%
Wagner 11%
Suppose that one of these requests is to be selected at random.
(a) What is the probability that the request is for one of the three B's?
(b) What is the probability that the request is not for one of the two S's?
(c) Neither Bach nor Wagner wrote any symphonies. What is the probability that the request is for a composer who wrote at least one symphony?
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7. –/3 points Notes Question: PeckDevStat6 6.E.032.
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Refer to the following information on births in the United States over a given period of time.
Type of Birth Number of Births
Single birth 39,000,000
Twins 700,000
Triplets 3000
Quadruplets 150
Use the information in the table to approximate the probabilities of the following events.
(a) A randomly selected pregnant woman who reaches full term delivers twins. (Give the answer to three significant figures.)
(b) A randomly selected pregnant woman who reaches full term delivers quadruplets. (Give the answer to three significant figures.)
(c) A randomly selected pregnant woman who reaches full term gives birth to more than a single child. (Give the answer to three significant figures.)
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8. –/2 points Notes Question: PeckDevStat6 7.E.012.
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A particular professor never dismisses class early. Let x denote the amount of time past the hour (minutes) that elapses before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 min. The density curve is shown in the following figure.
(a) What is the probability that at most 6 min elapse before dismissal?
(b) What is the probability that between 4 and 7 min elapse before dismissal?
You may need to use the appropriate table in Appendix A to answer this question.
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