Assignment #3 | Mathematics homework help

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 cm² 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 (S₁²/S₂²) computed from 10 measurements from type 1 (S₁²) and 8 measurements from type 2 (S₂²) will exceed 5.4.