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Chapter 4: Q74E (page 247)

Arrivals at an emergency room. Applications of the Poisson distribution were discussed in the Journal of Case Research in Business and Economics (December 2014). In one case involving a hospital emergency room, 2 patients arrive on average every 10 minutes. Let x = number of patients arriving at the emergency room in any 10-minute period. Assume that x has a Poisson distribution with mean 2. What is the probability that more than 4 patients arrive at the emergency room in the next 10 minutes?

Short Answer

Expert verified

The probability that more than 4 patients arrive at emergency room in next 10 minutes is 0.22.

Step by step solution

01

Given Information

Let x be the number of patients arriving at the emergency room on average every 10 minutes with mean 2

The p.m.f of the Poisson distribution is given by

pX=x=e-位位xx!;x=0,1,2,...0鈥�otw

02

 Compute probability 

The probability that more than four patients arrive is calculated as:

px猢�4=1-px<4=1-e-2200!+e-2211!+e-2222!+e-2233!=1-0.13+0.27+0.27+0.18=1-0.78=0.22

Therefore, the probability is 0.22.

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Most popular questions from this chapter

Types of finance random variables. Security analysts are professionals who devote full-time efforts to evaluating the investment worth of a narrow list of stocks. The following variables are of interest to security analysts. Which are discrete and which are continuous random variables?

a. The closing price of a particular stock on the New York Stock Exchange.

b. The number of shares of a particular stock that are traded each business day.

c. The quarterly earnings of a particular firm.

d. The percentage change in earnings between last year and this year for a particular firm.

e. The number of new products introduced per year by a firm.

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4.126 Wear-out of used display panels.Wear-out failure time ofelectronic components is often assumed to have a normaldistribution. Can the normal distribution be applied to thewear-out of used manufactured products, such as coloreddisplay panels? A lot of 50 used display panels was purchasedby an outlet store. Each panel displays 12 to 18 colorcharacters. Prior to the acquisition, the panels had been usedfor about one-third of their expected lifetimes. The data inthe accompanying table (saved in the file) give the failuretimes (in years) of the 50 used panels. Use the techniquesof this section to determine whether the used panel wear-outtimes are approximately normally distributed.

0.01 1.21 1.71 2.30 2.96 0.19 1.22 1.75 2.30 2.98 0.51

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3.50 1.16 1.62 2.18 2.84 3.50

The binomial probability distribution is a family of probability distributions with every single distribution depending on the values of n and p. Assume that x is a binomial random variable with n = 4.

  1. Determine a value of p such that the probability distribution of x is symmetric.
  2. Determine a value of p such that the probability distribution of x is skewed to the right.
  3. Determine a value of p such that the probability distribution of x is skewed to the left.
  4. Graph each of the binomial distributions you obtained in parts a, b, and c. Locate the mean for each distribution on its graph.\
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Identify the type of continuous random variable鈥攗niform,normal, or exponential鈥攄escribed by each of the following probability density functions:

a.f(x)=e-x77;x>o

b.f(x)=120;5<x<25

c.f(x)=e-.5[x-10/5]252蟺

Compute the following:

a.7!3!(7鈭�3)!

b.(94)

c. (50)

d.(44)

e.(54)
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