Miranda, a quality assurance inspector at a frozen treat factory, checks for product quality using a random sample of 11 frozen treats from a batch of 41, with 22 grape
popsicles and 19 cherry popsicles. Let p be the proportion of grape popsicles in the sample.
Part A: Is the 10% condition met in this case.
Part B: Is the Normal condition met in this case,
A) 10% condition not met in this case.
B) The Normal condition not met in this case.
A) If [tex]n\leq (\frac{1}{10})N[/tex] then 10% condition not met in this case
[tex]11\leq (\frac{1}{10} )41[/tex]
[tex]11 \leq 41[/tex]
So, 10% condition not met in this case.
B) n=11
p^ =[tex]\frac{x}{n} =\frac{22}{41}=0.5365[/tex]
np=11×0.5365
=5.9015<10
nq=11×(1-0.5365)=5.0985<10
So, both np and nq are less than 10
The normal condition is not met in this case.
Normal conditions are a restriction on philosophical arguments, especially in epistemology, in order to avoid objections perceived as digressive. As a reply to objections to an explanation of a phenomenon, e.g. a hypothesis or a theory, it is said, argument X holds [only] under normal conditions.
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