The weight of a medium-sized orange selected at random from a large bin of oranges at a local supermarket is a normally distributed random variable with mean μ = 12 ounces and standard deviation σ = 1.2 ounces. suppose we independently select two oranges at random from the bin. what is the probability that the difference in the weights of the two oranges exceeds 3 ounces?
Accepted Solution
A:
Let [tex]X_1[/tex] and [tex]X_2[/tex] represent the weights of the two oranges. Let [tex]d=X_1-X_2[/tex] represent the difference in weight. We're given that [tex]X_1[/tex] ~ N(12, 1.2^2) [tex]X_2[/tex] ~ N(12, 1.2^2)
Then, [tex]d~ N(12-12, 1.2^2 + 1.2^2) or N(0, 2*1.2^2)
So the standard deviation of d is [tex] \sqrt{2 \cdot 1.2^2} = 1.6971 [/tex]