## Related questions with answers

At the downtown office of First National Bank, there are five tellers. Last week, the tellers made the following number of errors each: 2, 3, 5, 3, and 5. a. How many different samples of 2 tellers are possible? b. List all possible samples of size 2 and compute the mean of each. c. Compute the mean of the sample means and compare it to the population mean

Solution

VerifiedNumber of errors made by tellers are : $2, 3, 5, 3$ and $5$.

$\textbf{a.}$

Total number of tellers in the population is $N=5$ and the sample size is $n=2$ Total number of possible samples of size 2 is

$\begin{align*} _NC_n&=\frac{N!}{n!(N-n)!}\\ &=\frac{5!}{2!(5-2)!}\\ &=\frac{5!}{2!3!}\\ &=10 \end{align*}$

Let $X_i$ be the $i^{th}$ sample of size $2$. So,

$\begin{align*} \bar{X}_i&=\frac{X_{i1}+X_{i2}}{2} \end{align*}$

$\textbf{b. }$Sample means for all possible samples of size $2$ is given in the below table.

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