Question

4. A company is deciding whether to fund research trials that, if successful, will earn the company some estimated profit. Suppose that each trial costs $50,000 and has a 20% success rate.

a. The company will keep funding the trials until it reaches the first success. What is the company’s expected cost and what is the standard deviation? (6 points)

b. What’s the probability that it will take three trials to reach the first success? (3 points)

Answer 1

a)

this number of trails X is Geometric distribution with parameter p=0.2

mean of distribution=μ=1/p=5

standard deviation σ=√(1-p)/p=

4.4721

let cost of the company is Y ; therefore Y=50000X

therefore   company’s expected cost E(Y) =50000*5 =250000

standard deviation of cost SD(Y )=50000*SD(X) =50000*4.4721 =223606.80

b)

probability that it will take three trials to reach the first success =P(1st 2 trail failure and 3rd success)

=(1-0.20)^2*0.2=0.128