Find the approximate probability that a randomly selected aspen tree in this park in 1975 would have a diameter less than 5.5 inches

The approximate probability that a randomly selected aspen tree in this park in 1975 would have a diameter less than 5.5 inches = 0.15866

Step-by-step explanation:

The complete question is presented in the attached image to this answer.

It is stated that the distribution of tree diameters is approximately normal, hence, this is a normal distribution problem with

Mean diameter = μ = 8 inches

Standard deviation = σ = 2.5 inches

The approximate probability that a randomly selected aspen tree in this park in 1975 would have a diameter less than 5.5 inches = P(x < 5.5)

To solve this, we first normalize or standardize 5.5 inches

The standardized score for 45mg/L is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (5.5 - 8)/2.5 = - 1.00

The required probability

P(x < 5.5) = P(z < -1.00)

We'll use data from the normal probability table for these probabilities

P(x < 5.5) = P(z < -1.00) = 0.15866

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