Question

a variable y of a finite population has the frequency distribution shown in the table. suppose a member is selected at random from the population and let y denote the value of the variable y for the member obtained. complete parts (a) through (d) below.

a. determine the probability distribution of the random variable y.

b. use random - variable notation to describe the events that y takes on the value 6, a value less than 6, and a value of at least 6.

the event that y takes on the value 6 can be represented as \\( \\{ y = 6 \\} \\).

the event that y takes on a value less than 6 can be represented as \\( \\{ y<6 \\} \\).

the event that y takes on a value of at least 6 can be represented as \\( \\{ y\geq6 \\} \\).

c. find \\( p(y = 6) \\), \\( p(y<6) \\), and \\( p(y\geq6) \\).

\\( p(y = 6)=\square \\) (type an integer or a decimal. do not round.)

Explanation:

Step1: Calculate total number of members

Total number of members \(n = 3 + 3+9 + 5=20\)

Step2: Calculate \(P(Y = 6)\)

Number of members with \(y = 6\) is \(f=9\). So \(P(Y = 6)=\frac{9}{20}=0.45\)

Answer:

\(0.45\)