Assignment Given a normally distributed population with a mean of 100 and a standard deviation of 20, find the following probabilities based on a sample of size 16: The National Health

1. Probability of a sample mean between 95 and 105

Z-scores for 95 and 105:

```
z(95) = (95 - 100) / 20 = -0.25
z(105) = (105 - 100) / 20 = 0.25
```

Probability:

```
P(-0.25 < Z < 0.25) = P(Z < 0.25) - P(Z < -0.25) = 0.5987 - 0.4013 = 0.1974
```

2. Probability of a sample mean less than 80

Z-score for 80:

```
z(80) = (80 - 100) / 20 = -1
```

Probability:

```
P(Z < -1) = 0.1587
```

3. Probability of a sample mean greater than 120

Z-score for 120:

```
z(120) = (120 - 100) / 20 = 1
```

Probability:

```
P(Z > 1) = 1 - P(Z < 1) = 1 - 0.8413 = 0.1587
```

4. Probability of a sample mean within 15 of the population mean

Z-scores for 85 and 115:

```
z(85) = (85 - 100) / 20 = -0.75
z(115) = (115 - 100) / 20 = 0.75
```

Probability:

```
P(-0.75 < Z < 0.75) = P(Z < 0.75) - P(Z < -0.75) = 0.7734 - 0.2266 = 0.5468
```

Explain the term paper on economic principles and their applications in farm management it's introduction objectives main body conclusion recommendations and references