decimal places tor the entire solution and final answers. 10. Use the following information to answer the next five questions: 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 \( X= \) the number of years a student will study ballet with the teacher. Let \( P(X) \) ?he probability that a student will study ballet \( \backslash(X) \) years. I \begin{tabular}{|c|c|c|c|c|c|c|} \hline\( x \) & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline\( P(X) \) & 0.10 & 0.05 & 0.10 & & 0.30 & 0.20 \\ \hline \end{tabular} a. In words, define the random variable \( X \). b. \( \quad P(X<4)= \) \( \qquad \) c. \( P(X<4)= \) \( \qquad \) d. On average, how many years would you expect a child to study ballet with this teacher? e. Find the standard deviation of the given situation.
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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. $\bullet$ Let $X=$ the number of years a student will study ballet with the teacher. $\bullet$ Let $P(x)=$ the probability that a student will study ballet $x$ years. Complete Table 4.28 using the data provided. $$\begin{array}{|c|c|}\hline x & {P(x)} & {x^{*} P(x)} \\ \hline 1 & {0.10} \\ \hline 2 & {0.05} \\ \hline 3 & {0.10} \\ \hline 4 & {} \\ \hline 5 & {0.30} \\ \hline 6 & {0.20} \\ \hline 7 & {0.10} \\ \hline\end{array}$$
Discrete Random Variables
Mean or Expected Value and Standard Deviation
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. $\bullet$ Let $X=$ the number of years a student will study ballet with the teacher. $\bullet$ Let $P(x)=$ the probability that a student will study ballet $x$ years. In words, define the random variable $X$.
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 $X=$ the number of years a student will study ballet with the teacher. ? Let $P(x)=$ the probability that a student will study ballet $x$ years. On average, how many years would you expect a child to study ballet with this teacher?
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