A4P2

A4P2#

In a city with \({{ params.N }}\) restaurants, only \({{ params.K }}\) of them have kids menus. Suppose a family visiting this city eats dinner at one of these restaurants chosen at random for a \({{ params.n }}\) days. Answer the following questions assuming they sample restaurants without replacement, that is, they do not visit a restaurant more than once. Round all answers to three decimal places.

Part 1#

(1 point) Let X denote the number of restaurants that the family visits within the week that have kids menus. What distribution does X follow?

Answer Section#

  • Bernoulli

  • Binomial

  • Poisson

  • Normal

  • Hypergeometric

Part 2#

(1 point) What is the support of this random variable?

Answer Section#

  • x = 0, 1, …, 8

  • x = 0, 1, …, 12

  • x = 0, 1, …, 4

  • x = 1, 2, …, 4

  • None of these

Part 3#

(1 point) What is the probability that less than half of the restaurants they visit have a kids menu?

Part 4#

(1 point) What is the expected number of restaurants with kids’ menus they visit during that week. Hint: you may use a result from the formula sheet.

Part 5#

(1 point) How would the probability in part 3 change if the family samples restaurants with replacement. That is, they permit themselves to revisit a restaurant.

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.