Question

A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The force in kilograms (kg) applied to the tablets varies a bit, with the N(11.7, 0.3) distribution. The process specifications call for applying a force between 11.5 and 12.5 kg.

(a) What percent of tablets are subject to a force that meets the specifications?
(b) The manufacturer adjusts the process so that the mean force is at the center of the specifications, mu = 11.8 kg. The standard deviation remains 0.2 kg. What percent now meet the specifications?

Answer 1

a) 74.5%

b) 93.3%

Step-by-step explanation:

μ = 11.7

σ = 0.3

standardize x to z = (x - μ) / σ

P( 11.5 < x < 12.5) =

P[( 11.5 - 11.7) / 0.2 < Z < ( 12.5 - 11.7) / 0.3] =

P( -0.67 < Z < 2.67) =

0.9962 - 0.2514 =

0.7448 = 74.5%

(From Normal probability table)

b)

μ = 11.8

σ = 0.2

standardize x to z = (x - μ) / σ

P( 11.5 < x < 12.5) =

P[( 11.5 - 11.8) / 0.2 < Z < ( 12.5 - 11.8) / 0.2]

P( -1.5 < Z < 3.5) =

0.9999 - 0.0668 =

0.9333 = 93.3%

(From Normal probability table)