Maths

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  • Topic: Normal distribution, Standard deviation, Random variable
  • Pages : 9 (1785 words )
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  • Published : January 10, 2013
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DUNDALK INSTITUTE OF TECHNOLOGY|
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Bachelor of Science in Computing in Applications & Support - Semester 3| Bachelor of Science in Computing in Networking & Support - Semester 3| Bachelor of Science in Computing in Software Development - Semester 3| |

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Data Analysis for Computing|
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Christmas 2010|
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Dr. Fiona Lawless|
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Answer any FOUR questions|
All questions carry equal marks|
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DO NOT TURN THIS PAGE UNTIL INSTRUCTED|

Question 1.
(a) The following 20 numbers relate to response times recorded when the new Carrolls network was being tested:

30.9| 41.1| 1.2| 30.6| 35.2| 25.8| 15.0| 35.8| 32.9| 20.7| 29.7| 12.4| 32.7| 33.5| 21.6| 38.9| 33.2| 17.9| 43.6| 41.2|

Using a class width of 10, construct a grouped frequency distribution for this data set and then estimate the mean response time. Explain why your answer is only an estimate of the mean of this data set. (5 marks)

(b) The numbers of SPAM EMAILS received by 750 DKIT computing students over a one week period, were recorded as follows:

No of SPAM EMAILS Received| Number of students |
less than 5| 68|
between 5 and 10| 176|
between 10 and 15| 244|
between 15 and 20| 193|
between 20 and 25| 42|
between 25 and 30| 27|

(i) Calculate the mean number of SPAM emails received by a computing student. (4 marks)

(ii) Construct a histogram for the data.
Use it to estimate the modal number of SPAM emails received. (3 marks)

(iii) Construct an Ogive for the given data set.
(3 marks)

(iv) Use your Ogive to estimate:
the median number of SPAM emails received; the interquartile range; the proportion of students who receivied 21 SPAM emails or more. (4 marks)

(v) Calculate the variance and standard deviation for the data. (6 marks)
(Total: 25 marks)

Question 2.

(a) The breakdown of applicants (by location & qualifications) for a post advertised by a Dundalk based computer company were as follows: Number of applicants| Dundalk| Dublin | Elsewhere|

Non-graduate| 57| 20| 15|
Graduate | 99| 69| 40|

If one of the applicants is selected at random, find the probability that he/she:
(i) is from Dublin
(ii) is a graduate from Dundalk
(iii) is either from Dundalk or Dublin
(iv) is a non-graduate or is from Dublin

If the applicant selected at random is from Dundalk. What is the probability that he/ she (vi) is a graduate?
(vii) is a graduate from Tralee?
(10 marks)
(b)
A game involves throwing a die:
E1: The face is 4,
E2: The face is even.
(i) Are these two events mutually exclusive?
(ii) Are these two events independent?
(5 marks)

(c) A computer lab contains 25 computers 3 of which are faulty. If two students enter this lab together and each selects a computer to work at, calculate the probability that (i) BOTH computers are defective;

(ii) NEITHER computer is defective;
(iii) EXACTLY ONE of the two computers is defective;
(iv) AT LEAST ONE of the two computers is defective.

(10 marks)
(Total: 25 marks)

Question 3.
(a) A soccer team has only two players who will take penalties. Player A takes 83% of all penalties and scores 75% of these. Player B takes the remainder and misses 39% of the penalties he takes.

If a penalty kick is taken, find the probability that: (i) the penalty is taken by player B;...
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