HW6CAS_skeleton

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.

Distribution is normal. Mean is 80, SD is 2
0.0668 (c)0.0179
0.7969

17.

Normal distribution. Mean is 64, SD is 4.907
0.7486
0.4052

19.

0.3520
Normal distrbution, mean is 266 and SD is 3.578
0.0465 (d)0.004
The sample came from a population with a lower average gestation period.
93.9

21.

0.3085
0.0418
0.0071
The increased sample size will decrease the standard deviation resulting in a decreased probability.
The probability of a random sample is 0.1056. The program isn’t very effective.
93.9

23.

0.5675
0.7291
0.8051
0.8351
The likelihood will increase.

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.

normal distribution, mean is 0l8, SD is 0.046
0.1922
0.0047

12.

Normal distribution, mean is 0.65 and SD 0.034
0.1867
0.0375

13.

Normal distribution, mean 0.035, Sd is 0.015
0.0040
0.0233

14.

Normal distribution, mean is 0.042 and SD is 0.013
0.0102
0.0606