# Contractor X is developing his bidding strategy against Contractor Y. The ratio of Y's bid price to X's cost for the 30 previous bids in which Contrac

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Contractor X is developing his bidding strategy against Contractor Y. The ratio of Y's bid price to X's cost for the 30 previous bids in which Contractor X has competed against Contractor Y is given in the Table

 Ration of Y’s bid Price of X’s cost Number of bids 1.02 6 1.04 12 1.06 3 1.10 6 1.12 3

Based on the bidding behaviour of the Contractor Y, the probability of winning against Contractor Y at a mark up of 8% for the next project is

1. 100%
2. 0%
3. more than 50% but less than 100%
4. more than 0% but less than 50%

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Correct Answer - Option 4 : more than 0% but less than 50%

Explanation:

 The ratio of Y's bid price to X's cost Mark-up of Y's bid Number of bids 1.02 2% 6 1.04 4% 12 1.06 6% 3 1.10 10% 6 1.12 12% 3 Total (Σn) =30

Mean of the bid to total cost ratio;

$\mu = \left[ {\frac{{1.02 \times 6 + 1.04 \times 12 + 1.06 \times 3 + 1.10 \times 6 + 1.12 \times 3}}{{30}}} \right] = 1.058$

Standard deviation,

$\sigma = \sqrt {\frac{{{\text{Σ }}{{\left( {{x_i} - \mu } \right)}^2}}}{N}}$

$= \sqrt {\frac{{6{{\left( {1.02 - 1.058} \right)}^2} + 12{{\left( {1.04 - 1.058} \right)}^2} + 3{{\left( {1.06 - 1.058} \right)}^2} + 6{{\left( {1.10 - 1.058} \right)}^2} + 3{{\left( {1.12 - 1.058} \right)}^2}}}{{30}}}$

= 0.034

Thus, Z at 8% markup level = $\left( {\frac{{x - \mu }}{\sigma }} \right)$

$\left( {\frac{{1.08 - 1.058}}{{0.034}}} \right)$ = 0.0647

From normal deviate table;

 Z Probability (%) 0.60 72.6 0.70 75.8

By interpolation, probability for Z = 0.647

$= 72.6 + \left( {\frac{{75.8 - 72.6}}{{0.70 - 0.60}}} \right)\left( {0.647 - 0.60} \right)$

= 74.104%

Hence, the probability of winning against the competitor Y at 8% mark-up

= (1 - 0.74104)

= 0.25896

= 25.896%