A pharmaceutical company receives large shipments of aspirin tablets the accepta

Question

A pharmaceutical company receives large shipments of aspirin tablets the acceptance sampling plan is to randomly select and test 15tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets has a 5% rate of defects, what is the probability that this whole shipment will be accepted? the average number of field mice per acre in a 5-acre wheat field is estimated to be 10. Find the probability that fewer than 3 field mice are found on a given acre.

Explanation / Answer

Here

n=number of tablets =15

p=probability of defective=0.05

Accept the whole batch if there only one or none doesn't meet the specification.

You have to P(x=0 )+p(x=1)

Formula of binomial probability is

P(X=x)=nCx p^x * (1-p)^n-x

P(x=0)=15C0 * (0.05)^0 (1-0.05)^15

=1*1*(0.95)^15

=0.4633

P(X=1)=15C1*0.05^1*0.95^14

=15*0.05*0.95^14

=0.3658

Probability of whole shipment accepted =P(x=0)+P(X=1)

=0.4633+0.3658

=0.8391

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