Given:
1% rate of defects
There are a total of 21 tablets tested
We use binomial probability distribution to solve this particular problem.
The general formula for the binomial distribution is:
[tex]P\mleft(x\mright)=^nCx.p^x\cdot\mleft(1-p\mright)^{n-x}[/tex]
where x is the number of successes in n trials (In this problem, x is the number of defectives in a random sample of 21 tablets.)
We are told that a shipment will be accepted if at most one tablet doesn't meet the required specifications. That is, the number of defectives must be less than or equal to one i.e
[tex]P\mleft(\mright?\text{shipment }accepted)=P(0)+P(1)_{}[/tex]
Substituting we have:
[tex]\begin{gathered} P\mleft(\text{shipment accepted}\mright)=^{21}C_0\cdot\mleft(.01\mright)^0\cdot\mleft(1-.01\mright)^{21-0.}+^{21}C_1\cdot\mleft(.01\mright)^1\cdot\mleft(1-.01\mright)^{21-1}. \\ =\text{ }0.80972\text{ + 0.1718} \\ =\text{ 0.98152} \end{gathered}[/tex]
Answer:
0.98152
