Question

Suppose that the number of gallons of milk sold per day at a local supermarket are normally distributed with mean and standard deviation of 319.9 and 26.4, respectively. What is the probability that on a given day the supermarket will sell between 304 and 305 gallons of milk

Answer 1

The probability that on a given day the supermarket will sell between 304 and 305 gallons of milk is 0.0127 or 1.27%

Explanation:

Normal Distribution

The graph of the Normal Distribution is also called the Bell Curve because of its particular shape. It occurs naturally in many real situations where a random variable needs to be modeled according to experimental results.

To evaluate the probability of a Normal Distribution, we need some kind of digital means because the formula cannot be computed directly in a formula. We'll use the MS Excel's specialized formula NORMDIST for the first value of x=304:

NORMDIST( 304 , 319.9 , 26.4 , true ) = 0.2735

Now for x=305:

NORMDIST( 305 , 319.9 , 26.4 , true ) = 0.2862

Both values are now subtracted to get the required probability

`P(304<x<305)=0.2862-0.2735=0.0127`

The probability that on a given day the supermarket will sell between 304 and 305 gallons of milk is 0.0127 or 1.27%