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

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 5E Chapter 3.3

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 5E

Problem 5E

If X is normally distributed with a mean of 6 and a variance of 25, find

Step-by-Step Solution:
Step 1 of 3

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

                        = 1.5403 - 1

                        = 0.5403

Hence, =0.5403.


c).

 =     

                        =

                           =

                           =

Here,  is obtained by using standard normal table(Area under normal curve). In Area under normal curve we have to see row 1.6 under column 0.00

  = 0.8849 In Area under normal curve we have to see row 1.2 under column 0.00

                           = 0.9452 - 0.8849

                           = 0.0603

Hence,  = 0.0603.


d).

= 1 -

                  = 1 -

                  = 1 -

                  = 1 -

                  = 1 -

Here,is obtained by using standard normal table(Area under normal curve).

In Area under normal curve we have to see row 3.0 under column 0.00  

                  = 1 - 0.9987

                  = 0.0013.

Hence, = 0.0013.


Step3 of 3:

e).

=

                        =

                        =

                        =     

                        =

                           =

                           =

Here,  is obtained by using standard normal table(Area under normal curve). In Area under normal curve we have to see row 1.0 under column 0.00

  = 0.1587 In Area under normal curve we have to see row -1.0 under column 0.00

                           = 0.8413 - 0.1587

                           = 0.6826

Hence, = 0.6826.


f).

                          =

                          =

                          =     

                       =

                          =

                          =

Here,  is obtained by using standard normal table(Area under normal curve). In Area under normal curve we have to see row 2.0 under column 0.00

  = 0.0228 In Area under normal curve we have to see row -2.0 under column 0.00

                          = 0.9772 - 0.0228

                          = 0.9544

Hence, 0.9544.


g).

=

                          =

                          =

                          =     

                       =

                          =

                          =

Here,  is obtained by using standard normal table(Area under normal curve). In Area under normal curve we have to see row 3.0 under column 0.00

  = 0.0013 In Area under normal curve we have to see row -3.0 under column 0.00

                          = 0.9987 - 0.0013

                          = 0.9974

Hence, 0.9974.

 


h).

=

                               =

                               =

                               =     

                            =

                               =

                              =

Here,  is obtained by using standard normal table(Area under normal curve).

Step 2 of 3

Chapter 3.3, Problem 5E is Solved
Step 3 of 3

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. This full solution covers the following key subjects: distributed, Find, mean, normally, variance. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. The full step-by-step solution to problem: 5E from chapter: 3.3 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. The answer to “If X is normally distributed with a mean of 6 and a variance of 25, find” is broken down into a number of easy to follow steps, and 16 words. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. Since the solution to 5E from 3.3 chapter was answered, more than 522 students have viewed the full step-by-step answer.

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