Question

Let ? represent the full height of a certain species of tree. Assume the distribution has mean 148.7 ft and standard deviation 92.3 ft. You intend to measure a random sample of ? = 118 trees.

a. Find the mean and standard deviation of the sample means. ?? =_______________ , ?? =_______________

b. The bell curve below represents the distribution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Sketch the graph and complete scale by indicating the values below each tic mark, correct to two decimal places.

Answer 1

Solution:

We are given µ = 148.7, σ = 92.3, n = 118

Part a

We know that the best estimate for the mean for sampling distribution of the sample means is given as the population mean, and the best estimate for the standard deviation for sampling distribution of the sample means is the standard error or σ/sqrt(n).

Mean of sample means = µ_x̄ = µ = 148.7

µ_x̄ = 148.7

Standard deviation of sample means = σ_x̄ = σ/sqrt(n) = 92.3/sqrt(118) = 8.496903723

σ_x̄ = 8.4969

Part b

Here, we have to draw the sampling distribution of the sample means described in above part. The required curve is given as below:

We have µ_x̄ = 148.7 and σ_x̄ = 8.50 (approximately) (rounded to two decimal)