Question

A government agency is putting a large project out for low bid. Bids are expected from 10 different contractors and will have a normal distribution with a mean of $3.5 million and a standard deviation of $0.25 million. Answer the following questions:

a.) What is the chance that one specific bidder bids less than $3.1 million?

b.) What is the probability that one specific bids more than $3.5 million?

c.) What is the probability that one specific bids more than $3 million?

c.) What is the probability that one specific bids more than $3.71 million?

d.) What is the probability that all bidders bid less than $3.76 million?

Answer 1

a) P(X < 3.1)

= P(z < (3.1 - 3.5)/0.25)

= P(z < -1.60)

= 0.0548

b) P(X > 3.5)

= P(z > (3.5 - 3.5)/0.25)

= P(z > 0)

= 0.50

c) P(X > 3)

= P(z > (3 - 3.5)/0.25)

= P(z > -2)

= 0.9772

d) P(X > 3.71)

= P(z > (3.71 - 3.5)/0.25)

= P(z > 0.84)

= 0.2005

e) Assuming all bidders bid are independent of each other:

P(One bidder bid less than $3.76 million)

= P(X < 3.76)

= P(z < (3.76 - 3.5)/0.25)

= P(z < 1.04)

= 0.8508

Hence,

P(All 10 bidders bid less than $3.76 million) = (0.8508)¹⁰ = 0.1987