A park ranger at a large national park wants to estimate the mean diameter of all the aspen trees in the park. The park ranger believes that due to environmental changes, the aspen trees are not growing as large as they were in 1975.

(a) 0.15866

(b) Clustered, with two peaks

(c) Point estimate is 6.3 inches

Margin of error is 0.7 inches

(d) Yes

(e) Stratified sampling method

Step-by-step explanation:

(a) The given information are as follows

Mean diameter of Aspen trees, μ = 8 inches

Standard deviation, σ = 2.5 inches

Therefore;

p(x < 5.5) = p(z < -1)

From the z score table, we have p = 0.15866

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

(b) The distribution of the Aspen trees can be described as clustered and having two peaks around 9.25 inches and 5.25 inches

(c) The point estimate is 5.6 + (7.0 - 5.6)/2 = 6.3

The margin of error = (7.0 - 5.6)/2 = 0.7 inches

(d) Yes, because the 8 inches is outside the range

(e) Stratified sampling method

Here, the Aspen trees are separated into the highland and lowland samples such that the measurement required will be representative of both highlands park and lowlands park.

77

step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq