Question

As Tanda’s dance coaching business has gotten more popular, she has come to book more and more group sessions. Each day she has 6 one hour slots available to book lessons. She charges $43 for a one hour session, plus $7 per student (including the first). Of course, if she books no students she doesn’t get paid. The distribution for the number of students she books each hour is as follows:

X	P(X=x)
0	0.27
1	0.42
2	0.16
3	0.11
4	0.04

1. How much does she charge for a one hour session with 3 students?
2. What is the expected number of students she will have in a single hour?
3. What is Tanda’s expected income per hour?
4. What is the standard deviation of Tanda’s hourly income when she is working?
5. How many time slots should she expect to have vacant each working day?
6. How much money should Tanda expect to bring in each day in total?
7. What is the standard deviation of Tanda’s daily income? We can assume that the number of students each hour is independent, but note that the standard deviations of independent variables can NOT be directly added together, even if we add the variables themselves.

Answer 1