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.
complete table 4.28 using the data provided.

x	p(x)	x*p(x)
1	0.10
2	0.05
3	0.10

|4|

5	0.30
6	0.20
7	0.10

is the following table correct?

Explanation:

Step1: Calculate \(x*P(x)\) for \(x = 1\)

\(1\times0.10=0.10\)

Step2: Calculate \(x*P(x)\) for \(x = 2\)

\(2\times0.05 = 0.10\)

Step3: Calculate \(x*P(x)\) for \(x = 3\)

\(3\times0.10=0.30\)

Step4: Calculate \(x*P(x)\) for \(x = 4\)

Since \(P(4)\) is not given, assume \(P(4)=1-(0.10 + 0.05+0.10 + 0.30+0.20 + 0.10)=0.15\), then \(4\times0.15 = 0.60\)

Step5: Calculate \(x*P(x)\) for \(x = 5\)

\(5\times0.30=1.50\)

Step6: Calculate \(x*P(x)\) for \(x = 6\)

\(6\times0.20 = 1.20\)

Step7: Calculate \(x*P(x)\) for \(x = 7\)

\(7\times0.10=0.70\)

The completed table:

\(x\)	\(P(x)\)	\(x*P(x)\)
2	0.05	0.10
3	0.10	0.30
4	0.15	0.60
5	0.30	1.50
6	0.20	1.20
7	0.10	0.70

Answer:

The completed table is shown above.