ENGI 3423 Probability and Statistics

Faculty of Engineering and Applied Science
2008 Fall

Term Test 1

2008 October 01
[Descriptive Statistics, Elementary Probability, Bayes’ Theorem]

1. Forty-five (45) observations of the displacement (in millimetres) of the final position of a faulty shock absorber from its neutral position are summarized in this boxplot:

   

   [Note:   no working is required in parts (a), (b) and (e) of this question.]

   1. Estimate, to the nearest integer, the lowest value.

      [2]

   2. Estimate, to the nearest integer, the median value.

      [2]

   3. Is the outlier mild or extreme?   Show your working.

      [6]

   4. Comment briefly on the outlier: is it suspect?   Why or why not?

      [3]

   5. Does the boxplot provide evidence for positive skew, negative skew or no skew?

      [2]

   6. Given the summary statistics , calculate the sample standard deviation s, correct to three significant figures.

      [5]

2. A contractor has bids out on three projects.
   Let A = (contractor wins the bid on project #1),
   B = (contractor wins the bid on project #2) and
   C = (contractor wins the bid on project #3).
   The following probabilities are known:
   P[A] = .60 ,     P[B] = .50 ,     P[C] = .40 ,
   P[AB] = .30 ,    P[BC] = .20 ,     P[CA] = .25 and
   the probability that the contractor is successful on all three bids is .15 .

   1. Find the probability that the contractor is successful in none of the three bids.

      [6]

   2. Is the set of three events   A, B, C   independent?   Show your working.

      [4]

3. The following probabilities are known:
   

   1. Find   P[X | Y],   expressed as a fraction in its lowest terms.

      [6]

   2. Find the odds that neither X nor Y occurs, expressed as a fraction in its lowest terms.

      [4]

4. 52 resistors in a bin are identical except for the manufacturer’s mark.
   Four resistors from each of 13 manufacturers are in the bin.
   Five resistors are drawn at random from the bin without replacement.
   Calculate the odds that four of the five resistors are from the same manufacturer.

   [+4]