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.

y
p(y = y)
3
.1
4
.1
5
.6
6
.2

b. use random - variable notation to describe the events that y takes on the value 5, a value less than 5, and a value of at least 5. the event that y takes on the value 5 can be represented as \\{y = 5\\}. the event that y takes on a value less than 5 can be represented as \\{y < 5\\}. the event that y takes on a value of at least 5 can be represented as \\{y \geq 5\\}. c. find p(y = 5), p(y < 5), and p(y \geq 5). p(y = 5)=\square (type an integer or a decimal. do not round.)

Explanation:

Step1: Calculate total number of members

Total number of members \(n = 1 + 1+6 + 2=10\)

Step2: Calculate \(P(Y = 5)\)

Number of members with \(y = 5\) is \(f=6\). Using the formula \(P(Y=y)=\frac{f}{n}\), we have \(P(Y = 5)=\frac{6}{10}=0.6\)

Answer:

\(0.6\)