Question

A bottling machine at a winery fills bottles of wine with an average of volume of 750 ml with a standard deviation of 6 ml. The volumes of the wine bottles are closely approximate by a normal curve. Find the following showing an appropriately labeled and shaded curve and calculator entries.

1. 1. What proportion of the wine bottles have more than 760 ml of wine?
2. 2. You pick up a bottle that contains 762 ml of wine. What is that bottle's percentile rank in the group?
3. 3. You do not want to sell any bottles that are in the first quartile for volume as they are not full enough. What volume marks the cutoff for the first quartile?

Answer 1

Let X denote the volume of the wine bottles

We are given :

a.

We need to find : P(X>760)

We can use standard normal tables or use Excel function to compute the above probability:

Proportion of the wine bottles have more than 760 ml of wine = 0.0478 = 4.78 %

b.

We need to find : P(X<762)

We can use standard normal tables or use Excel function to compute the above probability:

Bottle's percentile rank in the group = 97.72 98 (approx.)

c.

Let Q₁ be the first quartile

We use Excel function "NORMSINV()"

Hence,

Volume that marks the cutoff for the first quartile = 746 ml