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?

Question

Mathematics

Ayers

12 February, 19:14

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?

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Newt · Answer 1

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.