Question

University of Michigan researchers B. Wilkinson, N. Diedrich and E. Rothman, and C. Drummond of Indiana-Purdue University in Fort Wayne studied the duration between goals scored by the University of Michigan hockey team its 40 game, 1996 championship season. They found that the time between scores could be characterized with an exponential distribution with λ = 0.10.

a. Find the mean and standard deviation for this distribution,

b. Michigan has just scored. What is the probability that

1. It will be more than 10 minutes before they score again.

2. It will be less than 5 minutes before they score again.

3. It will be between 6 and 8 minutes before they score again.

Answer 1

λ = 0.1

Using Excel function EXPON.DIST(x,λ,cumulative)

a. Mean = 1/λ = 1/0.1 = 10

Standard deviation = sqrt(2)/λ = sqrt(2)/0.1 = 14.142

b. Probability that it will be more than 10 minutes before they score again: P(x>10) = 1-P(x<=10)

= 1-EXPON.DIST(10,0.1,TRUE)

= 1-0.632

= 0.368

Probability that it will be less than 5 minutes before they score again: P(x<5) = P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)

= EXPON.DIST(4,0.1,TRUE)

= 0.330

Probability that it will be between 6 and 8 minutes before they score again: P(6<x<8) = P(x=6)+P(x=7)+P(x=8)

= EXPON.DIST(6,0.1,FALSE)+EXPON.DIST(7,0.1,FALSE)+EXPON.DIST(8,0.1,FALSE)

= 0.055+0.050+0.045

= 0.149