Question

Museum management. Refer to the Museum Management and Curatorship (June 2010) study of the criteria used to evaluate museum performance, Exercise 3.18 (p. 170). Recall that the managers of 30 leading museums of contemporary art were asked to provide the performance measure used most often. Of these 30 museums, 8 specified “total visitors” as the performance measure. Consider a random sample of 5 museums selected from the 30. How likely is it that none of the museums in the sample specified “total visitors” as the performance measure?

Short answer

The sample specified “total visitor” as the performance measure is 0.184.

Step-by-step solution

 Given Information

A random sample of 5 museums selected from the 30 is given.

$$\begin{gathered} N=30 \\ M=8 \\ n=5 \end{gathered}$$

Let x be the number of times “total visitor” is selected.

Hypergeometric distribution is used to solve the above problem.

Therefore,

$$\begin{gathered} \begin{array}{rcl}p\left(x=0\right)& =& \frac{\left(M \\ 0\right)\times \left(N-M \\ n-0\right)}{\left(N \\ n\right)}\\ & =& \frac{\left(8 \\ 0\right)\times \left(30-8 \\ 5-0\right)}{\left(30 \\ 5\right)}\\ & =& \frac{1\times 26334}{142506}\\ & =& 0.184\end{array} \end{gathered}$$

Hence, the sample specified “total visitors” as the performance measure is 0.184.