Question

A ballet instructor is interested in knowing what percent of each years 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 Find P(x=4). (Enter an exact number as an integer, fraction, or decimal.) P(x=4) =

Answer 1

P(x=4)=0.20.

Explanation:

The table represents a probability distribution.

A valid probability distribution has the following properties:

0. P(x)≥0

,

1. The sum of P(x) is always 1.

Let P(x=4) = y

By the second property stated above, we have that:

`\begin{gathered} 0.10+0.05+0.20+y+0.30+0.10+0.05=1 \\ 0.80+y=1 \\ y=1-0.80 \\ y=0.20 \end{gathered}`

Therefore, P(x=4)=0.20.