Midterm Review 02

Note: some answers may disagree because of rounding in the 3rd or higher decimal point

Chapter 5

Section 2

Q30

  1. 0.748
  2. 0.61
  3. 0.367
  4. 0.966
  5. 0.656

Q38

  1. This is binomial, n =100, p - .45
  2. The scores are not binomial - can take multiple values
  3. This is binomial, either you scored above average or not. p will be about 0.5 (assuming symmetric distribution) and n is about 45 (45% of 100)
  4. Not binomial, contiuous variable - maybe exponential?

Q44

  1. 0.172
  2. 0.656
  3. 0.656

Q46

  1. Odds to probability = 1/(2047 + 1) = 1/2048. Probability of 11 losses = \(1/2^{11} = 1/2048\). Yes he is correct.

  2. \(1/2^{13} = 1/8192\)

Chapter 6

Section 1

Q5

0.5

Q6

0.15

Q7

0.5

Q8

0.45

Q17

  1. 1/3
  2. 1/3
  3. 1/3

Q20

  1. 0.118
  2. 0.287
  3. 0.134
  4. 0.95

Section 2

Q49

[1] 0.238

Q50

[1] 0.507

Q51

Probability someone is as tall as Trump or taller:

[1] 0.0993

Q52

Yes slightly unusual, as abou 43% of presidents are taller than 6 feet while only 24% of the population.

Q56

[1] 0.0334

Q59

  1. lower 25%
[1] 270
upper 75%
[1] 286
  1. assume 6 months = 183 days

Probability is basically 0:

[1] 1.22e-15

Q61

  1. 0.5
  2. 0.261
  3. 0.091
  4. 0.001. Yes unusual - probability is low.

Section 3

Q17

[1] 0.0445

Q19

[1] 0.898

Q24

See Homework

Q28

  1. 0.009
  2. 0.012

Chapter 7

Section 3

Q23

  1. 0.494
  2. 0.006
  3. 0

Q25

  1. Mean: 75878, and SE 516.398
  2. [74845, 76911]
  3. 1.985^{-5}
  4. Yes this would be unusual, likely true average is not 75,878.

Q29

  1. Yes appropriate because the population is normally distributed.
  2. 0.057
  3. 21.954

Q32

See Homework

Section 5

Q26

Probability that \(\hat p \ge .83\):

[1] 0.0668

\(P(.76 \le \hat p \le .84)\):

[1] 0.954

Q27

[1] 0.834

Q28

[1] 0.0614

Q33

  1. proportion: 0.13, standard error 0.045
  2. 0.939
  3. 6.128^{-7}
  4. [0.041, 0.219]