Solution Found!
If X is normally distributed with a mean of 6 and a
Chapter 3, Problem 5E(choose chapter or problem)
If \(X\) is normally distributed with a mean of 6 and a variance of 25 , find
(a) \(P(6 \leq X \leq 12)\).
(b) \(P(0 \leq X \leq 8)\).
(c) \(P(-2<X \leq 0)\).
(d) \(P(X>21)\).
(e) \(P(|X-6|<5)\).
(f) \(P(|X-6|<10)\).
(g) \(P(|X-6|<15)\).
(h) \(P(|X-6|<12.41)\)
Equation Transcription:
Text Transcription:
X
P(6 < or = X < or = 12)
P(0 < or = X< or = 8)
P(−2<X < or = 0)
P(X>21)
P(|X−6|<5)
P(|X−6|<10)
P(|X−6|<15)
P(|X−6|<12.41)
Questions & Answers
QUESTION:
If \(X\) is normally distributed with a mean of 6 and a variance of 25 , find
(a) \(P(6 \leq X \leq 12)\).
(b) \(P(0 \leq X \leq 8)\).
(c) \(P(-2<X \leq 0)\).
(d) \(P(X>21)\).
(e) \(P(|X-6|<5)\).
(f) \(P(|X-6|<10)\).
(g) \(P(|X-6|<15)\).
(h) \(P(|X-6|<12.41)\)
Equation Transcription:
Text Transcription:
X
P(6 < or = X < or = 12)
P(0 < or = X< or = 8)
P(−2<X < or = 0)
P(X>21)
P(|X−6|<5)
P(|X−6|<10)
P(|X−6|<15)
P(|X−6|<12.41)
ANSWER:Solution 5E
Step1 of 3:
We have random variable X which follows normal distribution with mean 6 and variance 25.
That is
= 5.
We need to find,
a).
b).
c).
d).
e).
f).
g).
h).
Step2 of 3:
Let “X” be random variable which follows normal distribution with parameters .
That is X N()
X N()
The appropriate Z statistics is given by
Z = N()
a).
=
=
=
=
Here, is obtained by using standard normal table(Area under normal curve). In Area under normal curve we have to see row 1.2 under column 0.00
= 0.5000 In Area under normal curve we have to see row 0.0 under column 0.00
= 0.8849 - 0.5000
= 0.3849.
Hence, = 0.3849.
b).
=
=
=
=
Here, is obtained by using standard normal table(Area under normal curve). In Area under normal curve we have to see row 0.4 under column 0.00
= 0.8849 In Area under normal curve we have to see row 1.2 under column 0.00
= 0.6554 + 0.8849 - 1