Question

Upon studying low bids for shipping contracts, a microcomputer manufacturing company finds that intrastate contracts have low bids that are uniformly distributed between 23 and 29, in units of thousands of dollars. (a) Find the probability that the low bid on the next intrastate shipping contract is below $25,000. (Round your answer to four decimal places.) (b) Find the probability that the low bid on the next intrastate shipping contract is in excess of $28,000. (Round your answer to four decimal places.)

Answer 1

a) 0.3333 = 33.33% probability that the low bid on the next intrastate shipping contract is below $25,000.

b) 0.1667 = 16.67% probability that the low bid on the next intrastate shipping contract is in excess of $28,000.

Explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distribution has two bounds, a and b.

The probability of finding a value lower than x is given by:

`P(X < x) = (x - a)/(b - a)`

The probability of finding a value higher than x is given by:

`P(X > x) = (b - x)/(b - a)`

Uniformly distributed between 23 and 29

This means that
`a = 23, b = 29`

(a) Find the probability that the low bid on the next intrastate shipping contract is below $25,000.

`P(X < 25) = (25 - 23)/(29 - 23) = 0.3333`

0.3333 = 33.33% probability that the low bid on the next intrastate shipping contract is below $25,000.

(b) Find the probability that the low bid on the next intrastate shipping contract is in excess of $28,000.

`P(X > 28) = (29 - 28)/(29 - 23) = 0.1667`

0.1667 = 16.67% probability that the low bid on the next intrastate shipping contract is in excess of $28,000.