Question

1. A pharmaceutical company manufactures vitamin pills which contain an average of 507 mg of vitamin C.

a) At most what percent of the pills will have more than 513 mg of vitamin C? [3 marks]

b) If you know that standard deviation is 3 mg, how could you improve your estimation? [3 marks]

c) If you know as well that distribution of vitamin C is bell-shaped, how could you improve your estimation? [3 marks]

Answer 1

a)

At most we can have 50 % of pills

b)

Here the percentage will be mean + 2 sigma

= 2.5%

c)

µ =    507                  
σ =    3                  
                      
P ( X ≥   513.00   ) = P( (X-µ)/σ ≥ (513-507) / 3)              
= P(Z ≥   2.000   ) = P( Z <   -2.000   ) =    0.0228  

= 2.28%

Please revert in case of any doubt.

Please upvote. Thanks in advance