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

Question

2 years ago

12

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.

1 answer:

Julli [10] · Answer 1 · 2023-08-25T23:40:25+03:00

Answer:

20.33%

Step-by-step 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%