In the ICU nurses monitor patients' respirations per minute (RESPS), as it is one of the earliest indicators that a patient may be nearing death. The mean number of RESPS of a healthy adult is 15.8, with a standard deviation of 3.1. When measuring the RESPS of a single patient, the count may fluctuate greatly from one measurement to the next, so to have conclusive findings the mean of several samples of the patient's RESPS is used. RESPS below 10 typically raise concern

d. What is the probability that a healthy patient's RESPS are below 10 on a single measurement?

e. If the nurse takes 4 measurements of a healthy patient's RESPS, what is the probability that the mean RESPS of this sample is below 10?

f. Based on your answer from part b, why would it be safe to assume that a patient is near death if we did measure a mean RESPS less than 10 from 4 measurements?