Consider a machine that fills 275 gallon tanks of water. The owner discovers tha

Question

Consider a machine that fills 275 gallon tanks of water. The owner discovers that the machine does not always dispense exactly 275 gallons. Instead, they discover that it fills between 272 and 275 gallons. 25% of the time it will fill between 272 and 273 gallons of water, 20% of the time it fills between 273 and 274 gallons, and 55% of the time it fills between 274 and 275 gallons. (a) What is the random variable? Is this discrete or continuous?

(b) Give a probability distribution for this situation.

(c) What is the probability that a 275 gallon tank gets less than 272.5 gallons or more than 273.8 gallons of water?

Explanation / Answer

a) this is continuous distribution. As quantity of water can take every value between 272 and 275.

b)

f(x)=0.25 272<x< 273

0.2. 273<x<274

0.55. 274<x<275

C) p(x<272.5 or x> 273.8)

= P(x<272.5)+ p(x>273.8)

=0.25/2+0.2*(274-273.8)+ 0.55

=0.125+0.04+0.55

=0.715

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