Auntie Barbie's Yummies markets a two-pound box of assorted treats. Because of imperfections in their equipment, the actual weight of the box of treats has a continuous uniform distribution ranging from 31.8 to 32.6 ounces. What is the probability that a box weighs exactly 31 ounces?

the probability that a box weighs exactly 31 ounces is 0

Step-by-step explanation:

since the box has a continuous distribution (therefore there are infinite real numbers between 31.8 and 32.6 ounces), the probability of a exact value out of a infinite quantity is 0. Mathematically, since the probability for a random variable X to be between values of 'a' and 'b' for a continuous probability density function f (x) is

P (a≤X≤b) = ∫ₐᵇ f (x) dx

for b=a, then

P (X=a) = ∫ₐᵃ f (x) dx = 0

Nevertheless, since the value of 31 is outside the range of 31.8 and 32.6 ounces, the probability of a value outside the continuous distribution is also 0