Suppose T and Z are random variables A factory manager colle

Suppose T and Z are random variables. A factory manager collected data on the number of equipment breakdown per day. From those data, she derived the probability distribution shown to the right, where W denotes the number of breakdowns on a given day. Answer parts a through c. On average, how many breakdowns occur per day?

Solution

3a

P( -2.62<=T<=2.62)

= 1-(P(T<-2.62)+P(T>2.62))

=1-(0.09+0.09)

=0.82

3a)

P( Z >1.48) = (1-P(-1.48<z<1.48))/2

=(1-0.86)/2

= 0.07

4a).

X

P(X)

x*p(x)

(x-mean)^2*p(x)

0

0.7

0

0.08575

1

0.25

0.25

0.105625

2

0.05

0.1

0.136125

1.000

0.35

0.3275

0.572276

Mean

0.35

Variance

0.3275

SD

0.572276

Mean =0.35

SD=0.572 ( three decimals)

4b) 0.35 breakdown per day

4c) breakdown in one year =0.35*250

=87.5

X	P(X)	x*p(x)	(x-mean)^2*p(x)
0	0.7	0	0.08575
1	0.25	0.25	0.105625
2	0.05	0.1	0.136125
	1.000	0.35	0.3275
			0.572276
	Mean	0.35
	Variance	0.3275
	SD	0.572276