Question

The length of time before a seed germinates when falling on fertile soil is approximately Normally distributed with a mean of 600 hours and a standard deviation of 100 hours. What is the probability that a seed will take more than 720 hours before germinating? Round to two decimal places.
a. 0.16
b. 0.12
c. 0.88
d. 0.997

Answer 1

Answer:

b. 0.12

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 600, \sigma = 100$

What is the probability that a seed will take more than 720 hours before germinating?

This is 1 subtracted by the pvalue of Z when X = 720. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{720 - 600}{100}$

$Z = 1.2$

$Z = 1.2$ has a pvalue of 0.88.

1 - 0.88 = 0.12

So the correct answer is:

b. 0.12