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Multiple questions on probability and distributions

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(24) A study by the National Park Service indicates that 60% of the vacationers going to the Rocky Mountain region visit the Yellowstone Park, 30% visit the Tetons, and 15% visit both. What is the probability that a vacationer to Yellowstone will visit the Tetons?
a. 25%
b. 50%
c. 45%
d. 90%
e. None of the above

(25) The probability of you taking a vacation this year is 60% while the probability of me taking one is only 30%. The following are the probabilities associated with the type of vacations I take:
Caribbean Cruise .35
European Driving Tour .30
South American Resort .20
Alaska Fishing Camp .15

What is the probability that I'll take a European driving tour this year?
a. 9%
b. 18%
c. 30%
d. 64%
e. 70%

(26) A bottling company offers three kinds of delivery service - instant, same day and within five days. The profit per delivery varies according to the kind of delivery according to the following table:
Type of Delivery # of Deliveries during Quarter Profit per Delivery
Instant 50 \$60
Same day 30 \$80
Within 5 days 20 \$130

What is the weighted mean profit per delivery?
a. \$80
b. \$110
c. \$137
d. \$90
e. None of the above

(27) Ten experts rated a newly developed chocolate chip cookie on a scale of 1 to 50. Their ratings were 34, 35, 41, 29, 27, 29, 32, 26, 39 and 40. What is the mean absolute deviation?
a. 3.76
b. 4.12
c. 4.60
d. 6.62
e. None of the above

(28) A sample of the monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical distribution. The sample mean is \$150 and the standard deviation is \$20. Assuming the distribution of monthly food expenditures is normal, about 99.7% of the monthly food expenditures are between what two amounts?
a. \$130 and \$170
b. \$90 and \$210
c. \$80 and \$220
d. \$110 and \$190
e. None of the above

(29) A sample of assistant professors on the business faculty at state supported institutions in Ohio revealed the mean income to be \$32,000 for 9 months with a standard deviation of \$3,000. Making no assumption about the probability distribution, what is the statistically expected proportion of faculty that earn less than \$26,000 or more than \$38,000?
a. 11%
b. 25%
c. 75%
d. 94%
e. None of the above

EXHIBIT 3: The following is the frequency distribution for the speeds of a sample of automobiles traveling on an interstate highway.

Speed
Miles per Hour Frequency
50 - 54 2
55 - 59 4
60 - 64 5
65 - 69 10
70 - 74 9
75 - 79 5

(30) Refer to Exhibit 3. The mean is
a. 65.5
b. 70
c. 68.5
d. 67
e. None of the above

(31) Refer to Exhibit 3. The variance is
a. 62.105
b. 54.071
c. 48.570
d. 50.000
e. None of the above

(32) A company is in the process of hiring new employees for its sales force. The Human Resource manager estimates that the following are the probabilities of how many sales people will be hired during a three month period:

No. To Be Hired Probability
0 5%
1 10%
2 15%
3 20%
4 30%
5 15%
6 5%

What is the expected number of new hires over a three-month period?
a. 2.95
b. 3.25
c. 3.45
d. 4.0
e. None of the above

(33) In question #32, how many people should be expected to be hired with a 75% probability over any three-month period?
a. 1.12 to 5.83 persons
b. 1.74 to 4.76 persons
c. .23 to 6.28 persons
d. .76 to 5.97 persons
e. None of the above

(34) A TV watcher is asked to rank twelve Survivor contestants for first, second, third and fourth place finishing. What is the probability of the ranking of any four contestants?
a. 1/495
b. 1/5,940
c. 1/11,880
d. 1/33,200
e. None of the above

(35) A personnel officer has three candidates to fill eight positions. Assuming any candidate can fill any of the positions, what is the possible number of ways to fill the positions?
a. 56
b. 336
c. 1,344
d. 19,342
e. None of the above

EXHIBIT 4: The student body of a large university consists of 60% female students. A random sample of 8 students is selected.

(36) Refer to Exhibit 4. What is the probability that among the students in the sample exactly two are female?
a. 0.0896
b. 0.2936
c. 0.0413
d. 0.0007
e. None of the above

(37) Refer to Exhibit 4. What is the probability that among the students in the sample at least 6 are male?
a. 0.0413
b. 0.0079
c. 0.0007
d. 0.0499
e. None of the above

EXHIBIT 5: The credit card balance of one elderly group is normally distributed with a mean of \$200 and a standard deviation of \$25.

(38) Referring to Exhibit 5, the probability of an elderly person from this group having a credit card balance of more than \$241.25 is
a. 0.0252
b. 0.0495
c. 0.0901
d. 0.9010
e. None of the above

(39) Refer to Exhibit 5. What percent of elderly people in this group would we expect to have balances between \$180 and \$220?
a. 28.81%
b. 45.88%
c. 57.62%
d. 64.23%
e. None of the above

EXHIBIT 6: The starting debt balances for new dentists are normally distributed with a mean of \$40,000 and a standard deviation of \$5,000.

(40) Refer to Exhibit 6. What is the probability that a randomly selected new dentist will have a starting debt balance of at least \$47,500?
a. 0.1534
b. 0.7564
c. 0.0668
d. 0.1053
e. None of the above

(41) Refer to Exhibit 6. What percentage of new dentists will have starting debt balances between \$34,000 and \$46,000?
a. 38.49%
b. 39.59%
c. 69.76%
d. 76.98%
e. None of the above

EXHIBIT 7: A particular county in Louisiana experienced incidents of West Niles virus at an average rate of 2.6 per month.

(42) Refer to Exhibit 7. What is the probability of at least three persons coming down with West Niles virus during a month?
a. 12.26%
b. 21.76%
c. 26.40%
d. 48.16%
e. None of the above

(43) Refer to Exhibit 7. What is the probability of an incident occurring every 15 days or less (assume a 30-day month)?
a. 27.25%
b. 45.53%
c. 65.67%
d. 72.75%
e. None of the above

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Solution Summary

This solution deals with 19 various multiple choice questions related to statistics, probability, and distributions. The full answers are given, along with the formulas to show how to get the final answers.

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