Question

The amount of fill X put into bottles of a particular brand of apple juice can be described by a normal model with mean E(X) = μ = 34 ounces and standard deviation SD(X) = σ = .85 ounces. What is the median amount of apple juice put into a bottle, that is, what is the amount k such that P(X > k) = P(X < k) = 0.50?

Answer 1

Solution:

Given, the Normal distribution with,

   = 34

= 0.85

Let k be the median.

So that ,

P(X > k) = P(X < k) = 0.50

Consider ,

P(X < k) = 0.50

P[(X - )/ <  (k - )/] = 0.50

P[Z <  (k - 34)/0.85] = 0.50

But from z table , P(Z < 0.00) = 0.50

Comparing these two equations we get ,

(k - )/ = 0.00

k = + (0.00 * ) = = 34

The median amount of apple juice put into a bottle is 34

{Observe that , for normal distribution ,

mean = mode = median

}