A pharmaceutical company produces tablets containing 50mg of active ingredient.
ID: 3335870 • Letter: A
Question
A pharmaceutical company produces tablets containing 50mg of active ingredient. ,Tt is
specified that tablets should contain within 0.5mg of this quantity to be acceptable. It is
known that 5% of all tablets will be outside of the specification. A random sample of 10
tablets are selected from a batch of 5000 tablets and the number of tablets, X, outside of
Wbat is the probability none of the 10 randomly sampled tablets are outside the
specification?
What of the assumptions of a binomial distribution? Are they reasonable in this case?
What is the probability that 3 or more of the 10 randomly sampled tablets are outside
thespecification?
Note; You may use the following values from MATLAB: , .
binocdf(2,10,0.05) = 0.9885 and binopdf(2,10,0.05) = 0.0746.
What is the expected number of the 10 randomly sampled tablets that are outside the
specification?
A pharmaceutical company produces tablets containing 50mg of active ingredient. ,Tt is
specified that tablets should contain within 0.5mg of this quantity to be acceptable. It is
known that 5% of all tablets will be outside of the specification. A random sample of 10
tablets are selected from a batch of 5000 tablets and the number of tablets, X, outside of
Wbat is the probability none of the 10 randomly sampled tablets are outside the
specification?
What of the assumptions of a binomial distribution? Are they reasonable in this case?
’
What is the probability that 3 or more of the 10 randomly sampled tablets are outside
thespecification?
Note; You may use the following values from MATLAB: , .
binocdf(2,10,0.05) = 0.9885 and binopdf(2,10,0.05) = 0.0746.
What is the expected number of the 10 randomly sampled tablets that are outside the
specification?
the specification is recorded. X is to be modelled by a binomial distribution.
Explanation / Answer
The Binomial Distribution gives the probability mass of number of successes in a certain number of events. The underlying assumption is that each event is a Bernoulli process, i.e. a success or failure process with a constant probability of success.
Here, the corresponding Bernoulli process is whether a tablet will be within the specified weight limit or not. From the given data it can be learnt that the probability of success, i.e. probability that the weight is outside limit specified is,
p=5%=0.05
(Given 5% of tablets are outside the specifications)
Hence it is justified to use a binomial distribution to model the number of tablets outside the weight specified.
If X is a binomial with parameter p (probability of success in the Bernoulli process) and no of events N then
P(X=n)= CnN pn(1-p)n
where P denotes probability and C denotes Combination operator.
Here X ~ Bin(10,0.05) , where 10 is number of events (tablets chosen) and 0.05 is the probability of success (weight outside limit). X is the number of tablets outside limit.
Probability of all tablets within limit = P(X=0) = C0100.050(1-0.05)10= 0.5987 (approx.)
Probability that 3 or more of the tablets are outside limit = P(X>2)
= 1-P(X<=2)
= 1-[P(X=0)+P(X=1)+P(X=2)]
= 1-[0.5987+0.3151+0.0746]
=1-0.9885
=0.0115
Expected number of tablets outside the limit = E(X)
=Np ( Equation for expectation of Binomial Process)
=10 x 0.05
=0.5
Therefore 0.5 tables can be expected to be outside limit.
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