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(12, 0.3) distribution. The process specifications call for applying a force between 11.2 and 12.2 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, μ = 11.7 kg. The standard deviation remains 0.3 kg. What percent now meet the specifications?

Answer 1

Answer:

Mean = 12

Standard deviation = 0.3

a) P(11.2 < X < 12.2)

= P((11.2 - )/ < (X - )/ < (12.2 - )/)

= P((11.2 - 12)/0.3 < Z < (12.2 - 12)/0.3)

= P(-2.66 < Z < 0.66)

= P(Z < 0.66) - P(Z < -2.66)

= 0.7453 - 0.00914

= 0.7361

= 73.61%

b) P(11.2 < X < 12.2)

= P((11.2 - )/ < (X - )/ < (12.2 - )/)

= P((11.2 - 11.7)/0.3 < Z < (12.2 - 11.7)/0.3)

= P(-1.66 < Z < 1.66)

= P(Z < 1.66) - P(Z < -1.66)

= 0.9515 - 0.0484

= 0.9031

= 90.31%

NOTE:: I HOPE YOUR HAPPY WITH MY ANSWER....***PLEASE SUPPORT ME WITH YOUR RATING...

***PLEASE GIVE ME "LIKE"...ITS VERY IMPORTANT FOR ME NOW....PLEASE SUPPORT ME ....THANK YOU

** PLEASE PLEASE PLEASE PLEASE GIVE ME "LIKE"....