# Assignment #3

**Assignment #3**

**Sampling Distributions**

1. Forest type 1 has an average diameter of 35 cm and a standard deviation of 6 cm. Forest type 2 has an average diameter of 25 cm and a standard deviation of 5 cm. The distribution of the diameters is normal in both types.

1. What is the probability that a sample mean will be greater than 36 cm from type 1 if 20 trees are measured?

2. What is the probability that a sample variance is less than 19 cm^{2} from type 1 if 20 trees are measured?

3. Find the probability that the sample mean computed from 20 measurements from type 1 will exceed the sample mean computed from 25 measurements from type 2 by at least 11 cm.

4. Find the probability that the ratio of sample variances (S_{1}^{2}/S_{2}^{2}) computed from 10 measurements from type 1 (S_{1}^{2}) and 8 measurements from type 2 (S_{2}^{2}) will exceed 5.4.

**Answers 1**

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