Question

trials of a simulation
using the geometric probability
distribution after 500 trials, determine
the following probabilities. type your
answer in the blank space below.

1. ( p(x = 1) = 0.186 )
2. ( p(x > 1) = 0.814 )
3. what is ( p(x < 6) )?

(hint, complete 1000 trials button, red square with white circle image)
(table with x and p(x) values for x from 1 to 30+)
(check button)

Explanation:

Step1: Identify values for \( X = 1,2,3,4,5 \)

From the table, \( P(X = 1)=0.186 \), \( P(X = 2)=0.154 \), \( P(X = 3)=0.146 \), \( P(X = 4)=0.092 \), \( P(X = 5)=0.084 \)

Step2: Sum the probabilities

\( P(X < 6)=P(X = 1)+P(X = 2)+P(X = 3)+P(X = 4)+P(X = 5) \)
\( = 0.186 + 0.154 + 0.146 + 0.092 + 0.084 \)
\( = 0.186+0.154 = 0.34 \); \( 0.34 + 0.146 = 0.486 \); \( 0.486 + 0.092 = 0.578 \); \( 0.578 + 0.084 = 0.662 \)

Answer:

\( 0.662 \)