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Homework answers / question archive / 1)The information below is the number of daily emergency service calls made by the volunteer ambulance service of Walterboro, South Carolina, for the last 50 days

1)The information below is the number of daily emergency service calls made by the volunteer ambulance service of Walterboro, South Carolina, for the last 50 days

Economics

1)The information below is the number of daily emergency service calls made by the volunteer ambulance service of Walterboro, South Carolina, for the last 50 days. To explain, there were 22 days on which there were 2 emergency calls, and 9 days on which there were 3 emergency calls.

 

  1. Convert this information on the number of calls to a probability distribution.

 

 

 

  1. Is this an example of a discrete or continuous probability distribution?
  2. What is the mean number of emergency calls per day?

 

  1. What is the standard deviation of the number of calls made daily?

 

 

 

 

 

 

 

 

 

 

2. Industry standards suggest that 10 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday.

 

  1. What is the probability that none of these vehicles requires warranty service? .

 

 

  1. What is the probability exactly one of these vehicles requires warranty service? .

 

  1. Determine the probability that exactly two or these vehicles require warranty service. .

 

 

  1. Compute the mean and standard deviation of this probability distribution.

 

 

 

 

3. The United States Postal Service reports 95 percent of first class mail within the same city is delivered within two days of the time of mailing. Six letters are randomly sent to different locations.

 

 

  1. What is the probability that all six arrive within two days?

 

  1. What is the probability that exactly five arrive within two days?

 

 

  1. Find the mean number of letters that will arrive within two days.

 

 

  1. Compute the variance and standard deviation of the number that will arrive within two days.

 

 

4. The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 70 percent of the cases. Suppose the 15 cases reported today are representative of all complaints.

.7

n = 15

 

  1. How many of the problems would you expect to be resolved today? What is the standard deviation?  

 

  1. What is the probability 10 of the problems can be resolved today?

 

 

  1. What is the probability 10 or 11 of the problems can be resolved today?

 

  1. What is the probability more than 10 of the problems can be resolved today?

 

5. In a Poisson distribution u= 0.4

 

  1. What is the probability that x= 0? 

 

  1. What is the probability that x > 0?

6. Automobiles arrive at the Elkhart exit of the Indiana Toll Road at the rate of two per minute. The distribution of arrivals approximates a Poisson distribution.

 

  1. What is the probability that no automobiles arrive in a particular minute? .

 

  1. What is the probability that at least one automobile arrives during a particular minute? .

 

 

7. For each of the following indicate whether the random variable is discrete or continuous.

 

  1. The length of time to get a haircut.
  2. The number of cars a jogger passes each morning while running.
  3. The number of hits for a team in a high school girls’ softball game.
  4. The number of patients treated at the South Strand Medical Center between 6 and 10 P.M. each night.
  5. The distance your car traveled on the last fill-up.
  6. The number of customers at the Oak Street Wendy’s who used the drive-through facility.
  7. The distance between Gainesville, Florida, and all Florida cities with a population of at least 50,000.

 

 

8.Recent statistics suggest that 15 percent of those who visit a retail site on the World Wide Web make a purchase. A retailer wished to verify this claim. To do so, she selected a sample of 16 “hits” to her site and found that 4 had actually made a purchase.

 

  1. What is the likelihood of exactly four purchases?

 

 

  1. How many purchases should she expect?

 

  1. What is the likelihood that four or more “hits” result in a purchase?

 

 

9.The position of chief of police in the city of Corry, Pennsylvania, is vacant. A search committee of Corry residents is charged with the probability of recommending a new chief to the city council. There are 12 applicants, 4 of which are either female or members of a minority. The search committee decides to interview all 12 of the applicants. To begin, they randomly select four applicants to be interviewed on the first day, and none of the four is female or a member of a minority. The local newspaper the Corry Press, suggests discrimination in an editorial. What is the likelihood of this occurrence? .141

 

 

 

10. Listed below is the population by state for the 15 states with the largest population. Also included is whether that state’s border touches the Gulf of Mexico, the Atlantic Ocean, or the Pacific Ocean (coastline).

 

  1. None of the states selected have any coastline? .

 

  1. Exactly one of the selected states has a coastline. .

 

 

 

  1. At least one of the selected states has a coastline.

 

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