Question

The heights of the trees in a forest are normally distributed, with a mean of 25 meters and a standard deviation of 6 meters. What is the probability that a randomly selected tree in the forest has a height greater than or equal to 37 meters? Use the portion of the standard normal table given to help answer the question.
z. Probability
0.00. 0.5000
0.50. 0.6915
1.00. 0.8413
2.00. 0.9772
3.00. 0.9987

0.13%
0.26%
2.3%
4.6%

Answer 1

Answer:

2.3%

Step-by-step explanation:

The formula to convert x into z distribution is

$z=\frac{x-\mu}{\sigma}$

Where z is the test statistic

x is what we are looking for (in this case 37)

$\mu$ is the mean (in this case, it is 25)

$\sigma$ is the standard deviation (we have 6)

Plugging these into the formula, we get:

$z=\frac{x-\mu}{\sigma}\\z=\frac{37-25}{6}\\z=2$

Thus we can say we want $P(z\geq 2)$

Note: $P(z\geq a)=1-P(z\leq a)$

The table given is for any  z where $P(z\leq a)$

Thus, now we have:

$P(z\geq 2)\\=1-P(z\leq 2)\\=1-0.9772\\=0.0228$

0.0228 into percentage is 0.0228 * 100 = 2.28%

Rounded, we get 2.3%

Third answer choice is right.