74% of all Americans live in cities with population greater than 100,000 people. If 37 Americans...

74% of all Americans live in cities with population greater than 100,000 people. If 37 Americans are randomly selected, find the probability that

a. Exactly 25 of them live in cities with population greater than 100,000 people.______

b. At most 26 of them live in cities with population greater than 100,000 people. _____

c. At least 27 of them live in cities with population greater than 100,000 people. _____

d. Between 23 and 29 (including 23 and 29) of them live in cities with population greater than 100,000 people._____

Expert Solution

Given that 74% of all Americans live in cities with a population greater than 100,000 people. Now if 37 Americans are randomly selected, then the distribution of the number of people(X) who lives in cities with a population greater than 100,000 people is Binomial(37,0.74)

a) The probability that exactly 25 of them live in cities with a population greater than 100,000 people = P(X=25) = 0.0957

b) The probability that at most 26 of them live in cities with a population greater than 100,000 people = P(X26) = 0.3609

c) The probability that at least 27 of them live in cities with a population greater than 100,000 people = P(X27) =

1- P(X26) = 0.6391

d) The probability that between 23 and 29 (including 23 and 29) of them live in cities with a population greater than 100,000 people = P(23X29) = P(X29) - P(X22) = 0.7452

orchestra answered 1 year ago

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