A certain university maintains a colony of male mice for research purposes. The ages of the mice are normally distributed with a mean of 60 days and a standard deviation of 5.2. Assume you randomly sample one mouse from the colony. The probability his age will be less than 45 days is _________.
A) 0.9980
B) 0.4980
C) 0.0020
D) 0.0019

Question

Quizplus · Accepted Answer

To find the probability of a randomly sampled mouse being less than 45 days old, we can use the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in (45 days), μ is the mean (60 days), and σ is the standard deviation (5.2 days).

z = (45 - 60) / 5.2 
z = -2.885

Using a standard normal distribution table (or a calculator), we can find that the probability of a z-score less than -2.885 is approximately 0.0020. Therefore, the probability of a randomly sampled mouse being less than 45 days old is 0.0020 or 0.2%.

The correct answer is C.

A Certain University Maintains a Colony of Male Mice for Research