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.
(type integers or decimals. do not round.)

Explanation:

Step1: Calculate the total number of members

The total number of members \( N=3 + 3+9 + 5=20\).

Step2: Calculate \(P(Y = 4)\)

The frequency of \(y = 4\) is \(f_4=3\). Using the formula \(P(Y=y)=\frac{f_y}{N}\), we have \(P(Y = 4)=\frac{3}{20}=0.15\).

Step3: Calculate \(P(Y = 5)\)

The frequency of \(y = 5\) is \(f_5=3\). Using the formula \(P(Y=y)=\frac{f_y}{N}\), we have \(P(Y = 5)=\frac{3}{20}=0.15\).

Step4: Calculate \(P(Y = 6)\)

The frequency of \(y = 6\) is \(f_6=9\). Using the formula \(P(Y=y)=\frac{f_y}{N}\), we have \(P(Y = 6)=\frac{9}{20}=0.45\).

Step5: Calculate \(P(Y = 7)\)

The frequency of \(y = 7\) is \(f_7=5\). Using the formula \(P(Y=y)=\frac{f_y}{N}\), we have \(P(Y = 7)=\frac{5}{20}=0.25\).

Answer:

\(y\)	\(P(Y = y)\)
\(5\)	\(0.15\)
\(6\)	\(0.45\)
\(7\)	\(0.25\)