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In: Statistics and Probability

Question 4: (In this problem first find the probability by using SPSS and copy the output...

Question 4: (In this problem first find the probability by using SPSS and copy the output and then calculate the number of trees manually by using the probabilities.)

A certain variety of pine tree has a mean trunk diameter of μ= 150 cm, and a standard deviation of σ= 30 cm which is normally distributed. A certain section of a forest has 500 of these trees. Find Approximately

1. how many of these trees have a diameter smaller than 120

2. how many of these trees have a diameter greater than 160

3. how many of these trees have a diameter between 130 and 160.

4. how many of these trees have a diameter between 120 and 140.

Expert Solution

The following information about the mean and standard deviation has been provided:

We need to compute . The corresponding z-value needed to be computed:

Therefore,

We need to compute The corresponding z-value needed to be computed is:

Therefore, we get that

We need to compute . The corresponding z-values needed to be computed are:

Therefore, the following is obtained:

We need to compute . The corresponding z-values needed to be computed are:

Therefore, the following is obtained:

orchestra answered 2 years ago

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