Question

1) A COVID-19 information hot line receiving 60 phone calls per 15 minutes on average.

a. Find probability that there is no phone calls in a period of 2 minutes (minimum time needed to run to washroom).

b. Find probability that there exactly 20 calls in a period of 5 minutes.

2) Assume that the length (in days) of incubation period of the COVID-19 is approximated normal with mean 5.1 days and standard deviation 3.11 days.

a. When a person is exposed to the virus, what is the probability that symptoms, if any, will appear within 9 days?

b. In 10,000 cases, about how many will have incubation period longer than 14 days?

c. Assume that a group of independent 20 people just come back from a cruise ship where the COVID-19 was spread. After 14 days of quarantine and no one is found sick, what is the probability that at least one of these 20 people is still potentially contagious (i.e. the probability that at least one person whose incubation period is longer than 14 days).

3) A local hospital buy N95 masks from 4 manufacturers, 20% from Manufacturer A, 5% from Manufacturer B, 40% from Manufacturer C, and 35% from Manufacturer D. Unfortunately, 5% from Manufacturer A, 3% from Manufacturer A, 1% from Manufacturer C, and 4% from Manufacturer D are defective.

a. What is the percentage of the defective masks?

b. When one defective mask is found, what is the probability that this mask is from
Manufacturer C?

c. Are event "A randomly selected mask is made by Manufacturer C" and the event "the mask is defective" independent? Explain the reason.

Answer 1

We would be looking at Q1 all parts here as:

that is 4 questions per minute.

a) The probability that there is no call in a period of 2 minutes is computed here as: (Using Poisson Probability function )

b) Probability that there are exactly 20 calls in a period of 5 minutes is computed here as:

Therefore 0.0888 is the required probability here.