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 11.1 and 12.1 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, μμ = 11.6 kg. The standard deviation remains 0.3 kg. What percent now meet the specifications?
%?
a)
P(11.1 <= X <= 12.1) = P((12.1 - 11.7)/0.3) <= z <=
(12.1 - 11.7)/0.3)
= P(-2 <= z <= 1.33) = P(z <= 1.33) - P(z <= -2)
= 0.9082 - 0.0228
= 0.8854
Ans: 88.54%
b)
P(11.1 <= X <= 12.1) = P((12.1 - 11.6)/0.3) <= z <=
(12.1 - 11.6)/0.3)
= P(-1.67 <= z <= 1.67) = P(z <= 1.67) - P(z <=
-1.67)
= 0.9525 - 0.0475
= 0.905
Ans: 90.50%
A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and...
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