If X is normally distributed with a mean of 6 and a

Chapter 3, Problem 5E

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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)

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

                   

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