Question

Calculate the A company is studying the air gap in their bottles. The air gap is normally distributed with a mean of 9.26 and 0.333 standard deviour percentage of product above and below the specification limits of 9.0 +/-0.5. TTTT Paragraph Arial 3112pt) E.E.T. %DO Q ETES: TT. ---

Answer 1

The Z value is defined as (X-mean)/standard deviation where X is the specified points.

Here we have two values 9+/- 0.5.

Again calculating the Z value for X=9.5+0.5=10 (x1) and 9.5-0.5=9 (x2)

We get Z1=(10-9.26)/0.333=2.317.

Looking up the Z table or using =NORMSDIST(2.222) in excel we get that 98.7% corresponds to 10.

Hence 100-98.7%=1.3% of values are above 9.5+0.5 (10)

Similarly We get Z2=(9-9.26)/0.333=-0.7808

Looking up the Z table or using =NORMSDIST(-0.7808) in excel we get that 2.17% corresponds to 9.

Hence 2.17% of values lie below 9.5-0.5=9.

Hence the % of values between 9.5+/-0.5= 2.17%+1.3%=3.47%