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The data in the tables below were collected from first year students at a community college. The variable is "number of credit cards." If the table below is a complete probability distribution, what must be the value of T?
Number of Credit Cards (x) 0 1 2 3 4 5
Number of Students (f) 122 40 28 2 2 6
Probability P(x) 0.61 T 0.14 0.01 0.01 0.03
A. 0.4
B. 0.04
C. 0.2
D. 0.02

Respuesta :

Solution :

It is given that P(x) is said to be complete or proper probability distribution if it satisfies the following two ways :

1. [tex]$P(x) \geq 0$[/tex]

2. [tex]$\sum_z P(x) = 1$[/tex]

Now consider,

[tex]$\sum_z P(x) = 1$[/tex]

⇒ [tex]$P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)=1$[/tex]

⇒ [tex]$0.61+T+0.14+0.01+0.01+0.03=1$[/tex]

⇒ [tex]$0.8+T=1$[/tex]

⇒ [tex]$T=1-0.8$[/tex]

       = 0.2

Therefore, the value of T is 0.2

Thus, option (c) is correct.