When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: randomly select and test 56 batteries and determine whether each is within specifications. the entire shipment is accepted if at most 2 batteries do not meet specifications. a shipment contains 7000 batteries, and 1% of them do not meet specifications. what is the probability that this whole shipment will be accepted? will almost all such shipments be accepted, or will many be rejected?

98.1% chance of being accepted

Step-by-step explanation:

Given:

sample size,n=56

acceptance condition= at most 2 batteries do not meet specifications

shipment size=7000

battery percentage in shipment that do not meet specification= 1%

Applying binomial distribution

In this formula, a is the acceptable number of defectives;

 n is the sample size; 

p is the fraction of defectives in the population.  

Now putting the value

a= 2

n=56

p=0.01

=0.56960+0.32219+0.08949

After summation, we get 0.981 i.e. a 98.1% chance of being accepted.  As this is such a high chance, we can expect many of the shipments like this to be accepted!

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step-by-step explanation:

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