Question

Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent of each year's class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution.

- Let $\mathrm{x}=$the number of years a student will study ballet with the teacher.

- Let $\mathrm{P}\left(\mathrm{x}\right)=$the probability that a student will study ballet $\mathrm{x}$years.

On average, how many years would you expect a child to study ballet with this teacher?

Short answer

On average, a youngster will spend $4.5$years studying dance.

Step-by-step solution

Table for no of students and probability

Explanation

From table,

${\mathrm{x}}_1\mathrm{P}\left({\mathrm{x}}_1\right)=0.1$,${\mathrm{x}}_2\mathrm{P}\left({\mathrm{x}}_2\right)=0.1$,${\mathrm{x}}_3\mathrm{P}\left({\mathrm{x}}_3\right)=0.3$.

${\mathrm{x}}_4\mathrm{P}\left({\mathrm{x}}_4\right)=0.6$,${\mathrm{x}}_5\mathrm{P}\left({\mathrm{x}}_5\right)=1.5$,${\mathrm{x}}_6\mathrm{P}\left({\mathrm{x}}_6\right)=1.2$,${\mathrm{x}}_7\mathrm{P}\left({\mathrm{x}}_7\right)=0.7$.

$\mathrm{\mu }=\sum _{\mathrm{i}=1}^7{\mathrm{x}}_{\mathrm{i}}\mathrm{P}\left({\mathrm{x}}_{\mathrm{i}}\right)$

$=0.1+0.1+0.3+0.6+1.5+1.2+0.7$

$=4.5\mathrm{years}$