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. X bar is normal with a mu of 80 and a standard deviation of 2
  2. .0668
  3. .0179
  4. .7969

17.

  1. x bar is normally distributed with a normal mu and normal standard deviaton
  2. .7486
  3. .4052

19.

  1. .3520
  2. smapling distribution is normal with a mu Xbar of 266 and a standard deviation Xbar of 16 over square root of 29
  3. .0465
  4. .0040
  5. It would be very unlikely for that sample to be less than 260 days
  6. .9984

21.

  1. .3085
  2. .0418
  3. .0071
  4. Bigger sample size makes for a smaller probability
  5. P( Xbar > 92.8) = .1056, the program isnt good
  6. 93.9 words per minute

23.

  1. .5675
  2. .7291
  3. .8051
  4. .8531
  5. the likelyhood of earning a positive rate of return on stocks 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. The sample distrbution of P-hat is normal with a mu of .8 and a standard deviation of .046.
  2. .1922
  3. .0047

12.

  1. The sampling distributon of p-hat is normal with a mu of .65 and a standard deviation of .035
  2. .1867
  3. .0375

13.

  1. sampling distribution of p-hat is normal with a mu of .35 and a standard deviation of .015
  2. .0040
  3. .0233

14.

  1. sampling distribution is normal with my of p-hat being .42 and standard deviation of p-hat being .013
  2. .0102
  3. .0606

15.

  1. The sampling distribution is normal with a mu of .47 and standard deviation of .035
  2. .1977
  3. .0239

16.

  1. The sampling distribution of p-hat is normal, mu = .82 and standard deviation = .038
  2. .2177
  3. .0344

17.

  1. The sampling distribution of p-hat is normal, mu = .39 and standard deviation = .022
  2. .3228
  3. .3198
  4. .0838