ma316f03hw13

# ma316f03hw13 - MA 316 MATHEMATICAL PROBABILITY...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MA 316: MATHEMATICAL PROBABILITY ASSIGNMENT #13 SOLUTIONS: SECTIONS 6.2 and 6.3 (OPTIONAL) FALL 2003 6.14: If the observed value of ¯ X is 81.2 from a random sample of size n = 20 from N ( μ, 80), then a 95% confidence interval for μ is ¯ X- 1 . 96 σ √ n , ¯ X + 1 . 96 σ √ n ¶ = ˆ 81 . 2- 1 . 96 √ 80 √ 20 , 81 . 2 + 1 . 96 √ 80 √ 20 ! = (77 . 28 , 85 . 12) . 6.15: If ¯ X is the mean of a random sample of size n from a distribution that has mean μ and variance σ 2 = 10, then a 90% confidence interval for μ is ¯ X- 1 . 645 σ √ n , ¯ X + 1 . 645 σ √ n ¶ . Therefore if P ( ¯ X- 1 < μ < ¯ X + 1) = 0 . 90 then we must have 1 = 1 . 645 · 3 √ n . Solving for n gives n = 24 . 35 so let n = 25 . 6.16: If a random sample of size n = 17 from a normal distribution N ( μ,σ 2 ) yields ¯ x = 4 . 7 and s 2 = 5 . 76, we need to find a 90 percent confidence interval for μ . Since we don’t know μ or σ 2 we must use that the random variable T = ¯ X- μ S/ √...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

ma316f03hw13 - MA 316 MATHEMATICAL PROBABILITY...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online