Question

With the COVID-19 crisis, a manager is concerned with handling the amount of customers arriving to his store. The manager assumes that the number of customers, X, arriving per hour has a Poisson distribution with mean rate of 10 customers per hour. Use this distribution for exercises!

1. Use R to generate the pmf of X.

2. Use R to plot the pmf of X.

3. Give the probability that at least 11 customers arrive to the store in a given hour.

4. There are 10 cards face down on a table and 3 of them are aces. If 5 of these cards are selected at random, what is the probability that at least 2 of them are aces?

5. Defects in a certain type of aluminum screen appear on the average of one in 150 square feet. If we assume the Poisson distribution, find the probability of at most one defect in 230 square feet.

Answer 1

1)The PMF of is generated as below.

X P
0 4.539993e-05
1 4.539993e-04
2 2.269996e-03
3 7.566655e-03
4 1.891664e-02
5 3.783327e-02
6 6.305546e-02
7 9.007923e-02
8 1.125990e-01
9 1.251100e-01
10 1.251100e-01
11 1.137364e-01
12 9.478033e-02

Use the following R code.
X <- 0:12
P <- matrix(dpois(X,10),nrow=13)
dimnames(P) = list(X, c("P"))
P
2) The PMF is plotted below.

Use the following R code.

X <- 0:12
P <- matrix(dpois(X,10),nrow=13)

plot(1:1)
dev.new()
plot(X,P, type="h", col="blue", lwd=2, xlab="X", ylab = "P(X=x)", main="PMF of X")

3) The required probability is

Use the following R command.

1-ppois(10,10)

4) The probability 2/3 of them are aces is

The required probability is