The amount of pyridoxine (in grams) in a multiple vitamin is normally distribute

Question

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with   = 90 grams and = 35 grams.
A. What is the probability that a randomly selected vitamin will contain between 100 and 110 grams of pyridoxine?
B. What is the probability that a randomly selected vitamin will contain at least 120 grams of pyridoxine?
C. What is the probability that a randomly selected vitamin will contain less than 85 grams of pyridoxine?
D. Approximately 75% of the vitamins will have at least how many grams of pyridoxine?

Explanation / Answer

Solution:

= 90, = 35

A. P(100 < X < 110 ) = (100-90)/35 < P((x-)/ < (110-90)/35) = P(0.29 < Z < 0.57) = 0.1016

B. P(X < 120) = (P((x-)/ < (120-90)/35) = P(Z < 0.86) = 0.8051

C. P(X < 85) = (P((x-)/ < (85-90)/35) = P(Z < -0.14) = 0.4443

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