Question

Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the proportion of trees having a diameter less than 9 inches.

Answer 1

To find the proportion of trees with a diameter less than 9 inches in a forest area, calculate the z-score for 9 inches using the mean and standard deviation of the tree diameters. We can find that the proportion of trees having a diameter less than 9 inches is approximately 0.3264.

Step-by-step explanation:

To find the proportion of trees having a diameter less than 9 inches, we need to find the area under the normal distribution curve that corresponds to values less than 9 inches. We can use the standard normal distribution table or a statistical calculator to find the z-score for 9 inches, which represents the number of standard deviations away from the mean. The formula for calculating the z-score is:

z = (x - mean) / standard deviation

Plugging in the values, we get:

z = (9 - 10) / 2.2 = -0.4545

Using the standard normal distribution table or a calculator, we can find that the proportion of trees having a diameter less than 9 inches is approximately 0.3264.

Answer 2

0.32472

Step-by-step explanation:

Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the proportion of trees having a diameter less than 9 inches.

The formula for calculating a z-score is z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation

z = (9 - 10)/2.2

z = -1/2.2

= -0.45455

Probability value from Z-Table:

P(x ≤ 9) = P(x < 9)

= 0.32472

Therefore, the proportion of trees having a diameter less than 9 inches is

0.32472