Question

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?

Answer 1

the probability that a box weighs exactly 31 ounces is 0

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