HW8 Solutions

2 points each, 72 points total

5.15

1. 1 - (0.1587 + 0.1567) = 0.6826
2. 1 - (0.0228 + 0.0228) = 0.9544
3. 1 - (0.0154 + 0.2912) = 0.6934
4. 1 - (0.3372 + 0.0250) = 0.6378
5. 1 - 0.0099 = 0.9901
6. 1 - 0.0099 = 0.9901

5.16

1. 0.0721
2. 0.0594
3. 0.2514 - 0.0080 = 0.2434
4. 0.3707 - 0.0250 = 0.3457
5. 0.5
6. 1 - (0.0099 + 0.0668) = 0.9233

5.19

1. 1.645
2. 1.96
3. -1.96
4. 1.28
5. 1.28

5.20

1. -1.75
2. 1.96
3. 1.645
4. 1.53
5. -0.83
6. 2.50
7. 0
8. 2.53

5.24

1. P(-0.5 < Z < 0.5) = 
   1 - (0.3085 + 0.3085) = 0.3830
2. P(-2.5 < Z < -0.5) =
   0.3085 - 0.0062 =0.3023
3. P(1 < Z < 2.5) =
   0.1587 - 0.0062 = 0.1525
4. P(-1.6 < Z < 0.8) =
   1 - (0.0548 + 0.2119) = 0.7333
5. P(Z > 1.12) = .11314
6. P(Z > -1.69) = 1 - 0.0455 = 0.9545

1) Find the following binomial probabilities

1. P(X = 5 | p=0.5, n=10)
   
   0.2460
   
2. P(X < 5 | p=0.5, n=10)
   
   0.3770
   
3. P(X <= 5 | p=0.5, n=10)
   
   0.6230
   
4. P(3 < X <6 | p=0.5, n=10)
   
   0.4510
   
5. P(0.3 < <0.6 | p=0.5, n=10)
   
   = P(3 < X <6 | p=0.5, n=10)
   = 0.4510

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