27. It is well known that taste in humans includes sweet, sour, salty, and bitter. A lesser known fifth taste called umami was identified almost 100 years ago in Japanese seaweed broth. Umami is not easy to describe but is often characterized as full bodied, savory, or rich. Umami is caused by the free form of the amino acid glutamine. Scientists have identified both the specific receptors on the tongue for the umami taste and the particular nerves that transmit the signal to the brain and, therefore, have accepted umami as a legitimate taste. Not all people can identify the umami taste and most who cannot confuse it with saltiness. Suppose a population consists of 80% umami tasters. Find the probabilities of the following events.

(a) A random sample of 17 people has exactly 14 tasters.

(b) A random sample of 17 people has 14 or more tasters.

(c) A random sample of 17 people has less than 14 tasters.

(d) A random sample of 20 people has at least 16 tasters.

(e) A random sample of 25 people has 20 tasters.