Question

ACME manufacturing company has developed a fuel-efficient machine that combines pressure washing with steam cleaning. It is advertised as delivering 5 gallons of cleaner per minute. HOWEVER, a machine delivers an amount at random anywhere between 4.95 and 5.15 gallons per minute.Assume that Y, the amount of cleaner dispensed per minute, is a uniform random variable with probability density function [p.d.f.], f(y), given below. { 5 4.95 <= y <= 5.15f(y) = { { 0 otherwise(a) Find the probability that Y, the amount of cleaner dispensed per minute,is greater than 5 gallons per minute.(b) Find the expected value of Y, E(Y).(c) Find the variance value of Y, VAR(Y).

Answer 1

Answer:

a) 0.75

b)5.05

c)0.02

Step-by-step explanation:

a)

P(Y>5)=?

This part is solved in the given picture.

b)

The mean of a uniform distribution is (a+b)/2.

Where a=4.95 , b=5.15.

E(Y)=(4.95+5.15)/2

E(Y)=10.1/2

E(Y)=5.05.

c)

The variance of a uniform distribution is (b-a)²/2.

V(Y)=(5.15-4.95)²/2

V(Y)=0.2²/2

V(Y)=0.04/2

V(Y)=0.02.