In blasting soft rock such as limestone, the holes bored to hold the explosives

Question

In blasting soft rock such as limestone, the holes bored to hold the explosives are drilled with a Kelly bar. This drill is designed so that the explosives can be packed into the hole before the drill is removed. This is necessary since in soft rock the hole often collapses as the drill is removed. The bits for these drills must be changed fairly often. Let X denote the number of holes that can be drilled per bit. The density for X is given in Table 3.13. (a) Find f(8). (b) Find the table for F. (c) Use F to find the probability that a randomly selected bit can be used to drill between three and five holes inclusive. (d) Find P[x lessthanorequalto 4] and P[X

Explanation / Answer

8) a) as sum of probability should be 1: therefore:

0.02+0.03+0.05+0.2+0.4+0.2+0.07+f(8) =1

f(8)=1-0.97=0.03

b)table for cumulative distribution function F(x):

c)P(3<=X<=5) =F(5)-F(2) =0.7-0.05=0.65

d)P(X<=4)=F(4)=0.3

P(X<4)=F(3) =0.1

No they are different.

e)F(-3) =0 as F(X) is 0 below x=1.

F(10)=1; as F(x) is 1 above or equal to x=8

x 1 2 3 4 5 6 7 8 F(x) 0.02 0.05 0.1 0.3 0.7 0.9 0.97 1

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