Solution Found!
Let Z~N(0, 1). Find a constant c for whicha. P(Z? c) =
Chapter 4, Problem 3E(choose chapter or problem)
Let Z ∼ N (0, 1). Find a constant c for which
a. \(P(Z \geq c)=0.1587\)
b.\(P(c \leq Z \leq 0)=0.4772\)
c. \(P(-c \leq Z \leq c)=0.8664\)
d. \(P(0 \leq Z \leq c)=0.2967\)
e.\(P(|Z| \geq c)=0.1470\)
Equation transcription:
Text transcription:
P(Z \geq c)=0.1587
P(c \leq Z \leq 0)=0.4772
P(-c \leq Z \leq c)=0.8664
P(0 \leq Z \leq c)=0.2967
P(|Z| \geq c)=0.1470
Questions & Answers
QUESTION:
Let Z ∼ N (0, 1). Find a constant c for which
a. \(P(Z \geq c)=0.1587\)
b.\(P(c \leq Z \leq 0)=0.4772\)
c. \(P(-c \leq Z \leq c)=0.8664\)
d. \(P(0 \leq Z \leq c)=0.2967\)
e.\(P(|Z| \geq c)=0.1470\)
Equation transcription:
Text transcription:
P(Z \geq c)=0.1587
P(c \leq Z \leq 0)=0.4772
P(-c \leq Z \leq c)=0.8664
P(0 \leq Z \leq c)=0.2967
P(|Z| \geq c)=0.1470
ANSWER:Solution :
Step 1 of 5:
Given ZN(0,1)
Our goal is:
a). We need to find c, P(Zc)=0.1587
b). We need to find c, .
c). We need to find c, .
d). We need to find c,
e). We need to find c,
Now we have to calculate c value.
a).
Given, P(Zc)=0.1587.
Here we have to find c value.
P(Zc)=1-P(Z
c)
P(Zc)=1-P(Z
c)
P(Zc)= 0.1587
P(Zc)=1-0.1587
P(Zc)=0.8413
From the area under the normal table P(Z1)=0.8413.
Therefore c =1.