1. The fill volume of a regular can of soft drink ranges from 11.97 to 12.03 oun

Question

1. The fill volume of a regular can of soft drink ranges from 11.97 to 12.03 ounces and is uniformly distributed.

a) Sketch the distribution, calculate and include the height of the distribution on your sketch. (2 points)

b) Calculate the mean and the standard deviation of the fill volume, show calculations/working below. (1 point)

c) What is the probability that a randomly selected can contains more than 12.02 ounces of fluid? Show calculations/working below. (1 point)

d) What is the probability that the fill volume is between 11.99 and 12.01 ounces? Show calculations/working below. (2 points)

Explanation / Answer

1.

b = 12.03
a = 11.97

a.

The height is ?

The uniform dist' probability should sum to 1

So,

Area = probability =1

So, h(b-a) = 1
So, h (12.03-11.97) = 1
h = 1/.06 = 16.67

b.

Mean = b-a/2 = 12
stdev = (b-a)^2/12 = (12.03-11.97)^2/12 = .0003

c. P(X>12.02) = 12.02-11.97 / 12.03-11.97 = .05/.06 = 5/6

d. P(11.99<X<12.01) = 12.01-11.99/12.03-11.97 = 2/6 = 1/3

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