Question

A plumber loads his truck each morning with faucets that will be needed for the service calls and other emergency calls that come in that day. Based on past​ experience, the number of faucets required each day​ (N) has the following​ distribution: ​p(0)equals​.05; ​p(1)equals​.25; ​p(2)equals​.5; ​p(3)equals​.15; ​p(4)equals.05. The expected value of N is then 1.9 faucets required per day. Each faucet requires 25 minutes to install. What is the expected number of minutes the plumber will spend each day installing​ faucets?

Answer 1

Answer:

47.5 minutes.

Step-by-step explanation:

Data provided:

p(0) = 0.05

p(1) = 0.25

p(2) = 0.5

p(3) = 0.15

p(4) = 0.05

Time required by each faucet to install = 25 minutes

Therefore,

The expected number of minutes spent by the plumber each day installing faucets

= ∑ ( xp(x) × time )

= ( 0 × 0.05 × 25 ) + ( 1 × 0.25 × 25 ) + ( 2 × 0.5 × 25 ) + ( 3 × 0.15 × 25 ) + ( 4 × 0.05 × 25 )

= 6.25 + 25 + 11.25 + 5

= 47.5 minutes.