Question

Problem 4 A bailet 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 teachec, and Px) the probability that a student will study ballet for x years) Expand All x Pa) 2 0.2 0.2 0.25 0.05 6 0.1 7 0.15 a. (396) Complete the table using the data provided. b. (396) The probability that a student studies ballet with this teacher for three years- c. (3%) The probability that a student studies ballet with this teacher for less than three years .

Answer 1

a) Total sum of Probability P(x)= 1

P(x)= P(x1)+P(x2)+P(x3)+P(x4)+P(x5)+P(x6)+P(x7)

1=P(x1)+0.2+0.2+0.25+0.05+0.1+0.15

P(x1)=0.05

xP(x)= x*P(x)

b) The probability that a student studies with this teacher for three years: 0.2

c)The probability that a student studies with this teacher less than three years: P(x<3)= P(1)+P(2)= 0.05+0.2=0.25

d)The sum of the entries in the P(x) column: 1

e)