A forestry study found that the diameter of the trees in a forest is normally distributed with mean 34 cm with a standard deviation of 8 cm. A group of 4 trees will be used as timber if the average of the 4 trees diameter is not too thick or thin. Specifically it is desired for the mean diameter to be between 30 and 40 cm in diameter. Find the probability that a randomly chosen group of 4 trees can be used as timber

The probability that a randomly selected group of four trees can be used as timber is 4.5 × 10⁻⁵

Step-by-step explanation:

The given parameters are;

Mean = 34 cm

The standard deviation = 8 cm

The mean

The Z score is , which gives;

For x  = 30 we have;

P(x>30) = 1 - 0.30854 = 0.69146

For x = 40, we have

P(x < 40) = 0.77337

Therefore, the probability that the mean of four trees is between 30 and 40 is given as follows;

P(30 < x < 40) = 0.77337 - 0.69146 = 0.08191

The probability that a randomly selected group of four trees can be used as timber is given as follows;

Binomial distribution

28

step-by-step explanation:

because that's the answer

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.