Homework Chapter 6

Section 1

Q18

\[ f(x) = \frac{1}{b-a} = \frac{1}{50 - 25} = \frac{1}{25} \]

\[ P(x > 45) = (50 - 45) * \frac{1}{25} = 5/25 = .2 \]

\[ P(35 < x < 45) = (45 - 35) * \frac{1}{25} = 10/25 = .4 \]

\[ P(x < 40) = (40 - 25) * \frac{1}{25} = 15/25 = .6 \]

Q19

\[ P(x < 180) = 1 - e^{-\frac{1}{365} \times 180} = .39 \]

\[ P(x > 365) = e^{-365/365} = .37 \]

  • P(A) = battery 1 lasts
  • P(B) = battery 2 lasts

Assume A and B are independent

\[ P(A \cap B) = P(A)P(B) = .37 * .37 = 0.14 \]

Section 2

Q46-48

46

[1] 0.23803

47

[1] 0.1175152

48

The chance of seeing that in a boy is:

[1] 0.005196079

Less than 1% chance of observing a baby boy that was less than 10 pounds.

Q68

  1. 0.3085375

  2. 0.2417303

  3. Probabilty of more than 215 for 1: 0.0668072

2 people independently 0.0044632

Section 3

Q13

Using normal approximation:

[1] 0.5467453

Using Binom numbers

[1] 0.5460421

Q15

Normal approximation

[1] 0.2467814

Using Binom Numbers

[1] 0.2446628

Q24

RH prob = .15

Blood bank get 92 donors

  1. z score (10.5)
[1] -0.9635293

probability using approximation

[1] 0.167641

exact using binomial

[1] 0.1679402
  1. zscore lower (14.5)
[1] 0.204385

score upper (20.5)

[1] 1.956256

answer:

[1] 0.3938088
  1. z-score (use 11.5 or fewer are rh NEGATIVE)
[1] -0.6715507
[1] 0.2509349

Q28

exact

[1] 0.009470831

approximation

[1] 0.01237234

The approximation seems to slightly over estimate the real probability - very close though