Here is the syntax you can use to check your answers for Section 8.1. (Forward and Backward)

Say you want to know the \(Pr(\bar{X} < 5)\) and \(\bar{X} \sim \mathcal{N}(6,1.5)\)

pnorm(5, mean = 6, sd = 1.5 )
## [1] 0.2524925

Here is the syntax you can use to check if a “Backward” calculation is correct.

Say you know the probability to the left of \(\bar{x}\) = .04 and you want to know what the appropriate \(\bar{x}\) is. You also know that \(\bar{X} \sim \mathcal{N}(6,1.5)\)

qnorm(.04, mean = 6, sd = 1.5)
## [1] 3.373971

15.

  1. normal
  2. 0.0668
  3. 0.0179
  4. 0.7969

17.

  1. normal
  2. 0.7486
  3. 0.4052

19.

  1. 0.3520
  2. 3.578
  3. 0.0465
  4. 0.0040
  5. that would be unusual meaning this sample is from a mean gestation period of less than 266 days
  6. 0.9844

21.

  1. 0.3085
  2. 0.0418
  3. 0.0071
  4. increasing the sample size decreases probability, this is because when mean decreases n increases
  5. it isn’t unusual beccause of the probability 0.1056, meaning the new program isnt much more effective than the old one.
  6. 93.9wpm

23.

  1. 0.5676
  2. 0.7291
  3. 0.8051
  4. 0.8531
  5. chance of earning a positive rate of return increases as the investment time horizon increases

Here is the syntax you can use to check your answers for Section 8.2. (Forward and Backward)

Say you want to know the \(Pr (\hat{P} < .35)\) and \(\hat{P} \sim \mathcal{N}(.4,.07)\)

pnorm(.35, mean = .4, sd = .07 )
## [1] 0.2375253

Here is the syntax you can use to check if a “Backward” calcuation is corect.

Say you know the probability to the left of \(\hat{p}\) = .04 and you want to know what the appropriate \(\hat{p}\) is. You also know that \(\hat{P} \sim \mathcal{N}(.4,.07)\)

qnorm(.05, mean = 12, sd = 4)
## [1] 5.420585

Section 8.2

11.

  1. normal
  2. 0.1922
  3. 0.0047

12.

  1. 0.0337
  2. 0.1867
  3. 0.0384

13.

  1. normal
  2. 0.0040
  3. 0.0233

14.

  1. normal
  2. 0.0102
  3. 0.0606

15.

  1. normal
  2. 0.1977
  3. is unusual

16.

  1. normal
  2. 0.2578
  3. 0.455

17.

  1. normal
  2. 0.3228
  3. 0.3198
  4. not unusual