HW6_skeleton

7.2

• 1. standard normal distribution
• 2. α
• 3. P(X<45)= 0.6915
• 4. P(X≤38)= 0.4207
• 1. .0071

  2. .3336

  3. .9115

  4. .9998

• 1. .9987

  2. .9441

  3. .0375

  4. 0.0009

• 15. z=0.67
• 17. The two z-scores are -2.58 and 2.58.
• 18. The two z-scores are -1.88 and 1.88.
• 23. P(X>35)= 0.98

shadenorm(mu=50, sig=7, above = 35,col = "blue",dens = 150)

• 24. P(X>65)=0.0162

shadenorm(mu=50, sig=7, above = 65,col = "blue",dens = 150)

• 25. P(X≤45)=0.24

shadenorm(mu=50, sig=7, below = 45,col = "blue",dens = 150)

• 1. 0.87

  2. 0.0132

  3. 0.70

  4. 0.12

  5. 96.5%

  6. 3.59%

8.1

• 1. sampling distribution
• 2. μ, σ/√n
• 3. standard error of the mean
• 4. True
• 5. False
• 6. False
• 7. Shape=normal, center=30, and spread=2.53 so X̄~N(30,2.53)
• 8. No, the population does not need to be normally distributed because the Central Limit Theorem says that,“regardless of the shape of the underlying population, the sampling distribution of x̄ becomes approximately normal as the sample size, n,increases.” The sampling distribution is the approximate normal curve with μ(x̄)=50 and σ(x̄)=0.63.
• 9. μ(x̄)= 80, σ(x̄)=2
• 10. μ(x̄)=64, σ(x̄)=3
• 1. X̄~N(80,2)

  2. P(x̄>83)=0.0668

  3. P(x̄≤75.8)=0.0179

  4. P(78.3<x̄<85.1)=0.7969

• 1. P(z<260)=.3557

  2. X̄~N(266,3.578)

  3. P(x̄≤260)=.047

  4. P(x̄≤260)=.004

  5. There is a very low chance that a random sample of 50 pregnancies will result in a mean gestation period of 260 days or less.

  6. .9844