Getaway Travel Agency surveyed a random sample of 45 of their clients about their vacation plans. Of the clients surveyed, 21 expected that they would go on 3 vacations in the next year. There are 516 Getaway Travel Agency clients.

Based on the data, what is the most reasonable estimate for the number of Getaway Travel Agency clients who expect to go on 3 vacations in the next year?
Choose 1 answer:
(A) 45
(B) 241
(C) 275
(D) 467

Question

Getaway Travel Agency surveyed a random sample of 45 of their clients about their vacation plans. Of the clients surveyed, 21 expected that they would go on 3 vacations in the next year. There are 516 Getaway Travel Agency clients.

Based on the data, what is the most reasonable estimate for the number of Getaway Travel Agency clients who expect to go on 3 vacations in the next year?
Choose 1 answer:
(A) 45
(B) 241
(C) 275
(D) 467

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the most reasonable estimate for the number of clients who expect to go on 3 vacations in the next year, we use the proportion of clients who said they would in the survey. ‖ ‖ step 2 ⋮ The proportion from the survey is $\frac{21}{45}$. ‖ ‖ step 3 ⋮ We apply this proportion to the total number of clients, which is 516. ‖ ‖ step 4 ⋮ The calculation is $\frac{21}{45} imes 516$. ‖ ‖ step 5 ⋮ Simplifying the calculation gives us $\frac{21}{45} imes 516 = \frac{1204}{5} = 240.8$. ‖ ‖ step 6 ⋮ The most reasonable estimate is the whole number closest to 240.8, which is 241. ‖ ***B*** ∻Key Concept∻ ⚹Proportional Estimation⚹ ∻Explanation∻ ⚹To estimate the number of clients planning to take 3 vacations, we use the proportion of such clients in the survey sample and apply it to the total client population.⚹◊What is the formula for calculating the percentage of clients who plan to take 3 vacations in the next year based on the survey data?⍭ Generate me a similar question◊

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