A few years ago, before restaurants became non-smoking, it seemed really unfair
ID: 3021528 • Letter: A
Question
A few years ago, before restaurants became non-smoking, it seemed really unfair that restaurants only classified a few tables as non-smoking. Since only about 1/3 of the general population of adults smoked (at the time), this seemed really unfair. But was it? Consider a random group of 4 adults that go together to the restaurant. What is the probability that less than half the group smokes?
A few years ago, before restaurants became non-smoking, it seemed really unfair that restaurants only classified a few tables as non-smoking. Since only about 1/3 of the general population of adults smoked (at the time), this seemed really unfair. But was it? Consider a random group of 4 adults that go together to the restaurant. What is the mean number of people that smoke in that group of 4?
A few years ago, before restaurants became non-smoking, it seemed really unfair that restaurants only classified a few tables as non-smoking. Since only about 1/3 of the general population of adults smoked (at the time), this seemed really unfair. But was it? Consider a random group of 4 adults that go together to the restaurant. Calculate the standard deviation of the number of people that smoke in that group of 4, round to the hundredths.
Explanation / Answer
1.
This means at most 1 smokes out of 4.
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 4
p = the probability of a success = 0.333333333
x = the maximum number of successes = 1
Then the cumulative probability is
P(at most 1 ) = 0.592592593 [ANSWER]
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2.
u = mean = np = 1.333333333 [ANSWER]
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3.
s = standard deviation = sqrt(np(1-p)) = 0.942809042 [ANSWER]
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