Business Statistics

252 Business Statistics

Solution From the question  = 1.10 per hour and in an exponential distribution, prob-

abilities can be computed by the formula P(x  x

0

) =

0

−λx

e

. The value of  can

be obtained as

1 1

0.9090

1.10

= = =



.

(a)  = 0.9090 indicates that on an average, 0.9090 hours will elapse between

arrivals.

(b) The probability that at least 5 hours will elapse between arrivals can be com-

puted as

Prob(x  5/ = 1.10) =

0

−λx

e

= e

–1.10(5)

= 0.0040

(c) The probability that at least 3 hours will elapse between train arrivals is

Prob(x  3/ = 1.10) =

0

−λx

e

= e

–1.10(3)

= 0.0368

Figure 7.47 is the Minitab output exhibiting computation of cumulative ...