Answer:
0.4114
0.0006
0.1091
0.1957
Step-by-step explanation:
Given:
p = 0.7 n = 10
We need to determine the probabilities using table , which contains the CUMULATIVE probabilities P(X [tex]\leq[/tex] x).
a. The probability is given in the row with n = 10 (subsection x = 3) and in the column with p = 0.7 of table:
P(X [tex]\leq[/tex] 3) = 0.4114
b. Complement rule:
P( not A) = 1 - P(A)
Determine the probability given in the row with n = 10 (subsection x = 10) and in the column with p = 0.7 of table:
P(X [tex]\leq[/tex] 10) = 0.9994
Use the complement rule to determine the probability:
P(X > 10) = 1 - P(X[tex]\leq[/tex] 10) = 1 - 0.9994 = 0.0006
c. Determine the probability given in the row with n = 10 (subsection x = 5 and x = 6) and in the column with p = 0.7 of table:
P(X [tex]\leq[/tex] 5) = 0.8042
P(X [tex]\leq[/tex] 6) = 0.9133
The probability at X = 6 is then the difference of the cumulative probabilities:
P(X = 6) = P(X [tex]\leq[/tex] 6) - P(X [tex]\leq[/tex] 5) = 0.9133 — 0.8042 = 0.1091
d. Determine the probability given in the row with n = 10 (subsection x = 5 and x = 11) and in the column with p = 0.7 of table:
P(X [tex]\leq[/tex] 5) = 0.8042
P(X [tex]\leq[/tex] 11) = 0.9999
The probability at 6 [tex]\leq[/tex] X [tex]\leq[/tex] 11 is then the difference between the corresponding cumulative probabilities:
P(6 [tex]\leq[/tex] X [tex]\leq[/tex] 11) = P(X [tex]\leq[/tex] 11) - P(X [tex]\leq[/tex] 5) = 0.9999 — 0.8042 = 0.1957
