Chapter 13.7, Problem 11PPS

To determine

The sampling method used in this problem is valid or not and the numbers of people out of $7000$ expected to buy the T-shirts for next concert is to be calculated.

Answer to Problem 11PPS

Yes. The sampling method is valid. $1225$ numbers of people expected to buy the T-shirts for next concert out of $7000$ participants.

Explanation of Solution

Given:

  $\begin{array}{l}X=140\\ Y=800\\ N=7000\end{array}$

Concept Used:

From larger population, a sample member is selected according to the starting point but with the fix or specific interval in the probability sampling method is known as the systematic random sample method.

Calculation:

The sampling of students is valid. In this problem there is use of Systematic random sample which is a type of the unbiased sample because every ${10}^{th}$ person is surveyed as they are leaving the concert. And here from the $800$ people only $140$ people said yes to buy T-shirts.

Number of people whopeople said yes to buy the T-shirts for next concert out of $7000$ participantsare calculated as:

  $\begin{array}{l}{N}_Y=\frac{X}{Y}\times N\\ N_Y=\frac{140}{800}\times 7000\\ N_Y=1225\end{array}$

Conclusion:

Hencepeople whopeople said yes to buy the T-shirts for next concert out of $7000$ participants are calculated as $N_Y=1225$ .