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Thedatafrom a study of collusion in bidding within the construction industry is provided.

a.

The total number of contracts is 108.

Let X represents the number of Bidders.

The proportion of the contracts involved at most five bidders is computed as,

\(\begin{aligned}P\left( {X \le 5} \right) &= P\left( {X = 2} \right) + P\left( {X = 3} \right) + P\left( {X = 4} \right) + P\left( {X = 5} \right)\\ &= \frac{{n\left( {X = 2} \right) + n\left( {X = 3} \right) + n\left( {X = 4} \right) + n\left( {X = 5} \right)}}{N}\\ &= \frac{{7 + 20 + 26 + 16}}{{108}}\\ &= 0.638\\ &\approx 0.64\end{aligned}\)

Therefore, the proportion of the contracts involved at most five bidders is 0.64.

The proportion of the contracts involved at least five bidders is computed as,

\(\begin{aligned}P\left( {X \ge 5} \right) &= 1 - P\left( {X < 5} \right)\\ &= 1 - \left( {P\left( {X = 2} \right) + P\left( {X = 3} \right) + P\left( {X = 4} \right)} \right)\\ &= 1 - \left( {\frac{{n\left( {X = 2} \right) + n\left( {X = 3} \right) + n\left( {X = 4} \right)}}{N}} \right)\\ &= 1 - \frac{{7 + 20 + 26}}{{108}}\\ &= 1 - 0.49\\ &= 0.51\end{aligned}\)

Therefore, the proportion of the contracts involved at least five bidders is 0.51.

The datafrom a study of collusion in bidding within the construction industry is provided.

b.

The total number of contracts is 108.

Let X represents the number of Bidders.

The proportion of the contracts involved between 5 and 10 bidders, inclusively is computed as,

\(\begin{aligned}P\left( {5 \le X \le 10} \right) &= P\left( {X = 5} \right) + P\left( {X = 6} \right) + P\left( {X = 7} \right) + P\left( {X = 8} \right) + P\left( {X = 9} \right) + P\left( {X = 10} \right)\\ &= \frac{{n\left( {X = 5} \right) + n\left( {X = 6} \right) + n\left( {X = 7} \right)... + n\left( {X = 10} \right)}}{N}\\ &= \frac{{16 + 11 + 9 + 6 + 8 + 3}}{{108}}\\ &= 0.49\end{aligned}\)

Therefore, the proportion of the contracts between 5 and 10 bidders, inclusively is 0.49.

The proportion of the contracts involved strictly between 5 and 10 bidders is computed as,

\(\begin{aligned}P\left( {5 < X < 10} \right) &= P\left( {X = 6} \right) + P\left( {X = 7} \right) + P\left( {X = 8} \right) + P\left( {X = 9} \right)\\ &= \frac{{n\left( {X = 6} \right) + n\left( {X = 7} \right) + n\left( {X = 8} \right) + n\left( {X = 9} \right)}}{N}\\ &= \frac{{11 + 9 + 6 + 8}}{{108}}\\ &= 0.31\end{aligned}\)

Therefore, the proportion of the contracts strictly between 5 and 10 bidders is 0.31.

The datafrom a study of collusion in bidding within the construction industry is provided.

c.

Steps to construct a histogram are,

1) Determine the frequency or the relative frequency.

2) Mark the class boundaries on the horizontal axis.

3) Draw a rectangle on the horizontal axis corresponding to the frequency or relative frequency.

The histogram is represented as,

The features that can be observed from the above histogram are,

1)The histogram is unimodal; this implies that there is only one mode; that is 4.

2)The distribution is positively skewed.

3)The typical value of x is 5.

4) There are no outliers present in the data.