Ask question

# in Advanced Math New Covid-19 patients arrive at the emergency room in Sultan Qaboos Hospital at a mean arrival rate of 18.8 patients per hour. Use Poisson distribution to compute the probability that at least three new patients will arrive at the emergency room within a 15-minute interval? # in Advanced Math New Covid-19 patients arrive at the emergency room in Sultan Qaboos Hospital at a mean arrival rate of 18.8 patients per hour. Use Poisson distribution to compute the probability that at least three new patients will arrive at the emergency room within a 15-minute interval?

Question
Upper Level Math asked 2020-11-30
in Advanced Math
New Covid-19 patients arrive at the emergency room in Sultan Qaboos Hospital at a mean arrival rate of 18.8 patients per hour. Use Poisson distribution to compute the probability that at least three new patients will arrive at the emergency room within a 15-minute interval?

## Answers (1) 2020-12-01
Step 1
Given that,
New Covid-19 patients arrive at the emergency room in Sultan Qaboos Hospital at a mean arrival rate of 18.8 patients per hour.
Mean arrival rate in 15 minute can be calculated as follows:
$$\displaystyle\lambda=\frac{{19.9}}{{60}}\times{15}$$
=4.7
Step 2
The probability that at least three new patients will arrive at the emergency room within a 15-minute interval can be calculated as follows:
$$\displaystyle{P}{\left({X}\ge{3}\right)}={1}-{P}{\left({X}{<}{3}\right)}$$</span>
$$\displaystyle={1}-{\left[{P}{\left({X}={0}\right)}+{P}{\left({X}={1}\right)}+{P}{\left({X}={2}\right)}\right]}$$
$$\displaystyle={1}-{\left[\frac{{{e}^{{-{4.7}}}{4.7}^{{0}}}}{{{0}!}}+\frac{{{e}^{{-{4.7}}}{4.7}^{{1}}}}{{{1}!}}+\frac{{{e}^{{-{4.7}}}{4.7}^{{2}}}}{{{2}!}}\right]}$$
$$\displaystyle={1}-{e}^{{-{4.7}}}{\left[{1}+{4.7}+{11.045}\right]}$$
=1-0.1523
=0.8477
Thus, the probability that at least three new patients will arrive at the emergency room within a 15-minute interval is 0.8477.

### Relevant Questions asked 2021-03-07
M. F. Driscoll and N. A. Weiss discussed the modeling and solution of problems concerning motel reservation networks in “An Application of Queuing Theory to Reservation Networks” (TIMS, Vol. 22, No. 5, pp. 540–546). They defined a Type 1 call to be a call from a motel’s computer terminal to the national reservation center. For a certain motel, the number, X, of Type 1 calls per hour has a Poisson distribution with parameter $$\displaystyle\lambda={1.7}$$.
Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be:
a) exactly one.
b) at most two.
c) at least two.
(Hint: Use the complementation rule.)
d. Find and interpret the mean of the random variable X.
e. Determine the standard deviation of X. asked 2020-11-16
Advanced Math
A bipolar alkaline water electrolyzer stack module comprises 160 electrolytic cells that have an effective cell area of $$\displaystyle{2}{m}^{{2}}$$. At nominal operation, the current density for a single cell of the electrolyzer stack is 0.40 $$\displaystyle\frac{{A}}{{c}}{m}^{{2}}$$. The nominal operating temperature of the water electrolyzer stack is $$\displaystyle{70}^{\circ}$$ C and pressure 1 bar. The voltage over a single electrolytic cell is 1.96 V at nominal load and 1.78 V at 50% of nominal load. The Faraday efficiency of the water electrolyzer stack is 95% at nominal current density, but at 50% of nominal load, the Faraday efficiency decreases to 80%.
(Give your answer to at least three significant digits.)
Calculate the nominal stack voltage:
Answer in V
Calculate the nominal stack current:
Answer in A
Calculate the nominal power on the water electrolyzer stack:
Answer in kW asked 2020-12-30
You are interested in finding a 95% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 14 randomly selected physical therapy patients. Round answers to 3 decimal places where possible.
$$9 6 10 15 19 6 23 26 19 16 11 25 16 11$$
a. To compute the confidence interval use a t or z distribution.
b. With 95% confidence the population mean number of visits per physical therapy patient is between ___ and ___ visits.
c. If many groups of 14 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About ___ percent of these confidence intervals will contain the true population mean number of visits per patient and about ___ percent will not contain the true population mean number of visits per patient. asked 2021-04-23
To monitor the breathing of a hospital patient, a thin belt isgirded around the patient's chest. The belt is a200-turn coil. When the patient inhales, the area encircled by the coil increases by $$\displaystyle{39.0}{c}{m}^{{2}}$$. The magnitude of the Earth's magnetic field is 50.0uT and makes an angle of 28.0 degree with the plane of the coil. Assuming a patien takes 1.80s toin hale, find the magnitude of the average induced emf in the coilduring that time.
Do I use the equation $$\displaystyle{E}={N}\cdot{A}\cdot{B}{w}{\sin{{w}}}{t}$$? asked 2021-02-19
An electric heater is used to heat a room of a volume $$\displaystyle{62}{m}^{{3}}$$. Air is brought into the room at $$\displaystyle{5}^{\circ}$$ C and is changed completely twice per hour. Heat loss through the walls amounts to approximately 850 kcal/h. If the air is to be maintainedat $$\displaystyle{20}^{\circ}$$ C, what minimum wattage must the heater have? (The specific heat of air is about 0.17 kcal/kg*Co.) asked 2021-03-07
There is currently a global pandemic and many researchers and scientists are working assiduously to find a vaccine. Assume that Advanced Researcher, a company that is currently testing a few vaccines confirms an 80% chance of effectiveness of one of their vaccines.
Which probability distribution would you use to calculate the probability of success or failure of Advanced Researcher's vaccine if it were to be administered to people in society? asked 2021-02-14
Dayton Power and Light, Inc., has a power plant on the Miami Riverwhere the river is 800 ft wide. To lay a new cable from the plantto a location in the city 2 mi downstream on the opposite sidecosts $180 per foot across the river and$100 per foot along theland.
(a) Suppose that the cable goes from the plant to a point Q on theopposite side that is x ft from the point P directly opposite theplant. Write a function C(x) that gives the cost of laying thecable in terms of the distance x.
(b) Generate a table of values to determin if the least expensivelocation for point Q is less than 2000 ft or greater than 2000 ftfrom point P. asked 2021-04-25
The unstable nucleus uranium-236 can be regarded as auniformly charged sphere of charge Q=+92e and radius $$\displaystyle{R}={7.4}\times{10}^{{-{15}}}$$ m. In nuclear fission, this can divide into twosmaller nuclei, each of 1/2 the charge and 1/2 the voume of theoriginal uranium-236 nucleus. This is one of the reactionsthat occurred n the nuclear weapon that exploded over Hiroshima, Japan in August 1945.
A. Find the radii of the two "daughter" nuclei of charge+46e.
B. In a simple model for the fission process, immediatelyafter the uranium-236 nucleus has undergone fission the "daughter"nuclei are at rest and just touching. Calculate the kineticenergy that each of the "daughter" nuclei will have when they arevery far apart.
C. In this model the sum of the kinetic energies of the two"daughter" nuclei is the energy released by the fission of oneuranium-236 nucleus. Calculate the energy released by thefission of 10.0 kg of uranium-236. The atomic mass ofuranium-236 is 236 u, where 1 u = 1 atomic mass unit $$\displaystyle={1.66}\times{10}^{{-{27}}}$$ kg. Express your answer both in joules and in kilotonsof TNT (1 kiloton of TNT releases 4.18 x 10^12 J when itexplodes). asked 2021-02-23
1. A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 144 students who averaged 44.7 texts per day. The standard deviation was 16.5 texts. a. To compute the confidence interval use a ? z t distribution. b. With 98% confidence the population mean number of texts per day is between and texts. c. If many groups of 144 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population number of texts per day and about percent will not contain the true population mean number of texts per day. 2. You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately $$\displaystyle\sigma={40.4}$$ dollars. You would like to be 90% confident that your estimate is within 1.5 dollar(s) of average spending on the birthday parties. How many parents do you have to sample? n = 3. You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately $$\displaystyle\sigma={57.5}$$. You would like to be 95% confident that your estimate is within 0.1 of the true population mean. How large of a sample size is required? asked 2020-12-29
Annie and alvie have agreed to meet between 5pm and 6pm,for dinner at a local restaurant. Let X= Annie's arrival time, andY= Alvie's arrival time. Suppose X and Y are independant with eachuniformly distributed on interval [5,6]
a) What is the joint pdf of X and Y
b) What is the probability that they both arrive between 5:15 and 5:45
c)if the first one to arrive will wait only 10 mins beforeleaving to eat somewhere else, What is the probability that theyeat at that restaurant. (Hint: The event of interest is A={(x,y):|x-y|<=6}.]
...