Chapter 13.7, Problem 3CYP

To determine

To calculate: To find if the sampling method is valid and the find how many of $380$ people who had dinner at the restaurant ate dessert

Answer to Problem 3CYP

  $228$ people out of $380$ ordered dessert after their meals

Explanation of Solution

Given information: After finishing the meal, every fifth person that left the restaurant was surveyed whether they ordered dessert after their meals.

Formula Used:

Probability is defined as the likelihood of an event.

Probability is calculated as

  $\mathrm{Probability}=\frac{Event}{Outcomes}$

Calculation:

Given that every fifth person that left the restaurant was surveyed whether they ordered dessert after their meals.

Yes, the above sampling method is valid, as this is a random experiment

Also, given that out of $20$ people, $12$ said yes.

Now, probability that person ordered dessert after their meals is calculated as follows:

  $\begin{array}{l}P=\frac{12}{20}\\ P=\frac{3}{5}\end{array}$

Also, total people surveyed $=380$

Thus, number of people who ordered dessert after their meals is calculated as follows:

  $\begin{array}{l}Number=\frac{3}{5}\times 380\\ Number=3\times 76\\ Number=228\end{array}$

Conclusion:

Hence, $228$ people out of $380$ ordered dessert after their meals