In the town of Wooster, Ohio, it is known that 90% of the residents prefer the locally produced Woostershire brand sauce when preparing a Caesar salad. The other 10% of residents prefer another well-known brand.
30 residents are chosen at random by a pollster. Let the random variable represent the number of those 30 residents that prefer Woostershire brand sauce.
Suggest a suitable distribution for and comment on any necessary assumptions.
Find the probability that
The pollster knows that there is a greater than 97% chance of at least of the 30 residents preferring Woostershire brand sauce, where is the largest possible value that makes that statement true.
Find the value of .
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