Question

Weight uniformity regulations usually refer to weights of tablets lying within a certain range of the label claim. Suppose the weights of individual tablets are Normally distributed with mean 100 mg (label claim) and standard deviation 7 mg.

A) What weight value K could be quoted such that 99% of all tablets are heavier than K?

B) What weight values A and B could be quoted such 99% of all tablets lie between A and B (assume this interval is symmetric about the mean) What is the value of A?

C) What weight value is B from the previous question?

Answer 1

A) P(X > K) = 0.99

or, P((X - )/ > (K - )/) = 0.99

or, P(Z > (K - 100)/7) = 0.99

or, P(Z < (K - 100)/7) = 0.01

or, (K - 100)/7 = -2.33

or, K = -2.33 * 7 + 100

or, K = 83.69

B) P(A < X < B) = 0.99

or, P(-x < X < x) = 0.99

or, P(Z < Z < z) = 0.99

or, P(Z < z) - P(Z < -z) = 0.99

or, P(Z < z) - (1 - P(Z < z)) = 0.99

or, 2P(Z < z) = 1.99

or, P(Z < z) = 0.995

or, z = 2.58

or, (x - )/ = 2.58

or, (x - 100)/7 = 2.58

or, x = 2.58 * 7 + 100

or, x = 118.06

So the value of A is -118.06

C) The value of B is 118.06