HW6_skeleton

7.2

• 1. Standard normal distribution
• 2. a
• 3. 0.3085
• 4. 0.4207
• 1. 0.0071

  2. 0.3336

  3. 0.9115

  4. 0.9998

• 1. 0.9987

  2. 0.9441

  3. 0.0375

  4. 0.0009

• 15. 0.67
• 17. z1=-2.58, z2=2.58
• 18. z1=-1.88, z2=1.88
• 23. 0.9838

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

• 24. 0.0162

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

• 25. 0.2389

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

• 1. P(1000<=x<=1400)=0.8658

  2. P(x<1000)=0.0132

  3. 0.7002

  4. 0.1230

  5. 96%

  6. 4%

8.1

• 1. sample distribution
• 2. mu / sigma over square root n
• 3. standard error of the mean
• 4. T
• 5. F
• 6. F
• 7. sigma(xbar)=2.53, mu(xbar)=30 shape: normal center: mean=30 spread: the standard deviation of the sample mean is less than the standard deviation of the population
• 8. sigma(xbar)=0.63, mu(xbar)=50
• 9. sigma(xbar)=2, mu(xbar)=80
• 10. sigma(xbar)=3, mu(xbar)=64
• 1. sigma(xbar)=2, mu(xbar)=80 shape: normal center: mean=80 spread: the standard deviation of the sample mean is less than the standard deviation of the population

  2. P(xbar>83)=0.0668

  3. P(xbar<=75.8)=0.0179

  4. P(78.3<xbar<85.1)=0.7969

• 1. P(x<260)=0.3520

  2. mu(xbar)=266, sigma(xbar)=3.578

  3. P(xbar<=260)=0.0465

  4. P(xbar<=260)=0.004

  5. it would be unusual if comes from xbar=266

  6. P(256<=xbar<=276)=0.9844