The accompanying data came from a study of collusion in bidding within the construction industry. No. Bidders No. Contracts 2 6 3 20 4 24 5 18 6 13 7 7 8 5 9 6 10 2 11 1 (a) What proportion of the contracts involved at most five bidders? At least five bidders? (Round your answers to three decimal places.) at most five bidders at least five bidders (b) What proportion of the contracts involved between five and 10 bidders, inclusive? Strictly between five and 10 bidders? (Round your answers to three decimal places.) between five and 10 bidders, inclusive

a)

The proportion of contracts involved at most five bidders is 0.667.

The proportion of contracts involved at least five bidders is 0.51.

b)

The proportion of contracts involved between five and 10 inclusive bidders is 0.5.

The proportion of contracts involved strictly between five and 10 bidders is 0.304.

Step-by-step explanation:

No. bidders No. contracts Relative frequency of contracts

2 6 6/102=0.0588

3 20 20/102=0.1961

4 24 24/102=0.2353

5 18 18/102=0.1765

6 13 13/102=0.1275

7 7 7/102=0.0686

8 5 5/102=0.049

9 6 6/102=0.0588

10 2 2/102=0.0196

11 1 1/102=0.0098

Total 102

a)

We have to find proportion of contracts involved at most five bidders.

Proportion of at most 5 = Relative frequency 2 + Relative frequency 3 + Relative frequency 4 + Relative frequency 5

Proportion of at most 5=0.0588 + 0.1961+0.2353+0.1765

Proportion of at most 5=0.6667

The proportion of contracts involved at most five bidders is 0.667.

proportion of at least five bidders = proportion≥5 = 1 - proportion less than 5

Proportion less than 5=0.0588 + 0.1961+0.2353=0.4902

proportion of at least five bidders=1-0.4902=0.5098

The proportion of contracts involved at least five bidders is 0.51

b)

We have to find proportion of contracts involved between five and 10 inclusive bidders.

Proportion of contracts between five and 10 inclusive = Relative frequency 5 + Relative frequency 6 + Relative frequency 7 + Relative frequency 8 + Relative frequency 9 + Relative frequency 10

Proportion of between five and 10 inclusive=0.1765 + 0.1275 + 0.0686 + 0.049 + 0.0588 + 0.0196

Proportion of between five and 10 inclusive=0.5

The proportion of contracts involved between five and 10 inclusive bidders is 0.5

We have to find proportion of contracts involved strictly between five and 10 bidders.

Proportion of contracts strictly between five and 10 = Relative frequency 6 + Relative frequency 7 + Relative frequency 8 + Relative frequency 9

Proportion of strictly between five and 10=0.1275 + 0.0686 + 0.049 + 0.0588

Proportion of strictly between five and 10=0.3039

The proportion of contracts involved strictly between five and 10 bidders is 0.304.