Eastwood's BA201 Assignments

Homework Answers for Chapter 6 Exercises 31-40

31.       a.         15.39%, found by (8 – 10.3)/2.25 = – 1.02, then 0.5000 – 0.3461 = 0.1539

            b.         17.31%, found by:

                        z = (12 – 10.3)/2.25 = 0.76.  Area is 0.2764

                        z = (14 – 10.3)/2.25 = 1.64.  Area is 0.4495 

                        The area between 12 and 14 is 0.1731, found by 0.4495 – 0.2764.

            c.         Yes, but it is rather remote.  Reasoning:  On 99.73% of the days, returns are between 3.55 and 17.03, found by 10.3 ± 3(2.25).  Thus, the chance of less than 3.55 returns is rather remote.

 

32.        a.         0.0262, found by:  m =50(0.20) = 10

                        s 2 = 50(0.20)(0.80) = 8                            Then (4.5 – 10)/2.83 = – 1.94, for which the area is 0.4738.  Then 0.5000 – 0.4738 = 0.0262

            b.         0.9441, found by (5.5 – 10)/2.83 = – 1.59, for which the area is 0.4441.  Then 0.5000 + 0.4441 = 0.9441

            c.         0.0297, found by (4.5 – 10)/2.83 = – 1.94 and (5.5 – 10)/2.828 = – 1.59.  Then 0.4738 – 0.4441 = 0.0297

            d.         0.8882, found by adding the area between z = – 1.59 and z = 1.59.  Then 2(0.4441) = 0.8882

 

33.        a.         0.9678, found by:  m =60(0.64) = 38.4

                        s 2 = 60(0.64)(0.36) = 13.824                        Then (31.5 – 38.4)/3.72 = – 1.85, for which the area is 0.4678.  Then 0.5000 + 0.4678 = 0.9678

            b.         0.0853, found by (43.5 – 38.4)/3.72 = 1.37, for which the area is 0.4147.  Then 0.5000 – 0.4147 = 0.0853

            c.         0.8084, found by 0.4441 + 0.3643

            d.         0.0348 found by 0.4495 – 0.4147

 

34.        m =np = 100(0.05) = 5               s 2 = np(1 – p) = 100(0.05)(0.95) = 4.75           

           

            a.         0.1251, found by (7.5 – 5)/2.18 = 1.15.  The area is 0.3749.  Then 0.5000 – 0.3749 = 0.1251

            b.         0.1192, found by (10.5 – 5)/2.18 = 2.52.  The area is 0.4941.  Subtracting 0.4941 – 0.3749 = 0.1192

            c.         0.0714 calculating the probability of 8.5 and 7.5, then find the difference, probability of 8.5 = 0.4463, 7.5 is 0.3749 so 0.4463 – 0.3749 = 0.0714

            d.         0.0197, found by 0.5000 – 0.4803

 


35.        a.         0.8106, where m =10, variance = 8, standard deviation = 2.8284, z = (7.5 – 10)/2.823 = -0.88.  The area is 0.3106, then 0.5000 + 0.3106 = 0.8106

            b.         0.1087, found by z = (8.5 – 10)/2.823 = -0.53, then 0.3106 – 0.2019 = 0.1087

            c.         0.2981, found by 0.5000 – 0.2019

 

36.        a.         m =60(0.10) = 6            

                        z = (1.5 – 6)/2.32 = – 1.94                     z = (2.5 – 6)/2.32 = – 1.51

                        Probability is 0.4738 – 0.4345 = 0.0393

            b.         0.9738, found by 0.5000 + 0.4738

 

37.        0.0968, found by:  m =50(0.40) = 20

            s2 = 50(0.40)(0.60) = 12                       

            z = (24.5 – 20)/3.4641 = 1.30.  The area is 0.4032.  Then for 25 or more, 0.5000 – 0.4032 = 0.0968

 

38.        m =800(0.80) = 640                   

                           Probability is 0.5000 – 0.4850 = 0.0150

 

39.        a.         1.65 = (45 – m)/5           m =36.75

            b.         1.65 = (45 – m)/10         m =28.5

            c.         z = (30 – 28.5)/10 = 0.15, then 0.5000 + 0.0596 = 0.5596

 

40.        m =np=25(1/35) = 0.7143                  

                    Then 0.5000 + 0.1026 = 0.6026

 

 

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