Chapter 13.7, Problem 2GP

To determine

The numbers of defective watches from $2000$ watches and tell that the sampling used in the problem is valud or ot.

Answer to Problem 2GP

Yes. The sampling method is valid. $400$ are the defective watches from $2000$ watches.

Explanation of Solution

Given:

  $\begin{array}{l}Y\text{'}=2000\\ X=3\\ Y=15\\ X\text{'}=?\end{array}$

Concept Used:

Sampling method of the probability means that every member of the given target population has chance of being included in the sample. Either simple random or systematic sampling gets used by the sampling methods.

Calculation:

Here out of first $15$ watches, $3$ watches get defective which is simple sampling method. So, the sampling method used to find out the defective watches is valid.

Now find the number of defective watches out of $2000$ watches:

  $\begin{array}{l}\frac{X}{Y}=\frac{X\text{'}}{Y\text{'}}\\ \frac{3}{15}=\frac{X\text{'}}{2000}\\ X\text{'}=\frac{3}{15}\times 2000\\ X\text{'}=400\end{array}$

Conclusion:

Hence, number of defective watches out of $2000$ watches is $X\text{'}=400$ .