Question

The filling quantity of automatically filled spray bottles is a normally distributed random variable with the known parameters μ = 150cm3 and σ = 3.5cm * 3. In the Quality Control, a bottle is discarded if it contains no more than 146cm * 3.

The daily production of spray bottles amounts to 4000 pieces. a) How many spray bottles can be put on average every day? b) At what new value μ would the filling machine have to be adjusted, so that on average only 1% of the spray bottles are claimed in the quality control?

Answer 1

The filling quantity of automatically filled spray bottles is a normally distributed random variable with the known parameters μ = 150cm3 and σ = 3.5cm * 3. In the Quality Control, a bottle is discarded if it contains no more than 146cm * 3.

The daily production of spray bottles amounts to 4000 pieces. a) How many spray bottles can be put on average every day?

Z value for 146, z =(146-150)/3.5 = -1.14

P( x < 146) = P( z < -1.14) =0.1271

Therefore 12.71% are discarded.

0.1271*4000 =508 ( rounded) daily dicarded.

3492 spray bottles can be put on average every day.

b) At what new value μ would the filling machine have to be adjusted, so that on average only 1% of the spray bottles are claimed in the quality control?

Z value for bottom 1% = -2.326

Let x be Adjusted mean , x-2.326*3.5 = 146

Therefore x=154.14

= 154 cm * 3 ( rounded).