Question

Upon studying low bids for shipping contracts, a microcomputer manufacturing company finds that intrastate contracts have low bids that are uniformly distributed between 21 and 28, in units of thousands of dollars. a. Find the probability that the low bid on the next intrastate shipping contract is below $24,000. (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 $27,000. (Round your answer to four decimal places.)

Answer 1

a) 0.4286 = 42.86% probability that the low bid on the next intrastate shipping contract is below $24,000.

b) 0.1429 = 14.29% probability that the low bid on the next intrastate shipping contract is in excess of $27,000.

Explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x or equal is given by the following formula.

`P(X \leq x) = (x - a)/(b-a)`

The probability that we find a value X greater than x is given by the following formula.

`P(X > x) = 1 - (x - a)/(b-a)`

Uniformly distributed between 21 and 28

This means that
`a = 21, b = 28`

a. Find the probability that the low bid on the next intrastate shipping contract is below $24,000.

`P(X \leq 24) = (24 - 21)/(28 - 21) = 0.4286`

0.4286 = 42.86% probability that the low bid on the next intrastate shipping contract is below $24,000.

b. Find the probability that the low bid on the next intrastate shipping contract is in excess of $27,000.

`P(X > 27) = 1 - (27 - 21)/(28 - 21) = 0.1429`

0.1429 = 14.29% probability that the low bid on the next intrastate shipping contract is in excess of $27,000.