Question

The heights of fully grown sugar maple trees are normally distributed, with a mean of 87.5 feet and a standard deviation of 6.25 feet. Random samples of size 12 are drawn from the population. Find the probability that the mean height of the tree is less than 86 feet.

Answer 1

20.33%

Explanation:

We have that the mean (m) is equal to 87.5, the standard deviation (sd) 6.25 and the sample size (n) = 12

They ask us for P (x <86)

For this, the first thing is to calculate z, which is given by the following equation:

z = (x - m) / (sd / (n ^ 1/2))

We have all these values, replacing we have:

z = (86 - 87.5) / (6.25 / (12 ^ 1/2))

z = -0.83

With the normal distribution table (attached), we have that at that value, the probability is:

P (z <-0.83) = 0.2033

The probability is 20.33%