Question

If someone could help me with these two questions I would really appreciate it.

1. Lawrence books appointments at his exclusive HotHair salon so that customers arrive evenly. Let T be the arrival time for a customer chosen at random and suppose T is uniform on (0, 9).    What is the standard deviation of T?

2. Suppose the number of Hurricanes Level 4 or greater making landfall in the Gulf Cost and Florida per year is a Poisson with standard deviation of 1.4. What is the probability one or more such Hurricanes make landfall next year?

2.

Answer 1

Solution:

Question 1)

Given: T be the arrival time for a customer chosen at random and suppose T is uniform on (0, 9).

That is: T ~ Uniform( a = 0 , b = 9)

We have to find the standard deviation of T.

SD(T)=1/(0-a)2 SDITEV 12

SD(T) = V (9-02 12

SD(T) = ། l. |ལ

SD(T) = V IZ

SD(T) = 6.75

SD(T) = 2.5981

( Round answer to specified number of decimal places)

Question 2)

Given: the number of Hurricanes Level 4 or greater making landfall in the Gulf Cost and Florida per year is a Poisson with standard deviation of 1.4.

For Poisson distribution , standard deviation is given by:

SD= A

1.4 = VA

(v) = 351

1.96 =

that is:

= 1.96

Mean and Variance of Poisson distribution are same

thus

Mean= per year.

= 1.96

We have to find  the probability one or more such Hurricanes make landfall next year

=.........?

P(X > 1)

P(X > 1) = 1 - P(X <1)

P(X > 1) = 1 - P(X = 0)

Thus find P(X=0) by using Poisson distribution.

Probability mass function of Poisson distribution is:

e-l x P(X = 1) = x

e-1.96 X 1.960 P(X = 0) = ?

P(X = 0) = 0.1408584 x 1

P(X =0) = 0.1408584

Thus

P(X > 1) = 1 - P(X = 0)

P(X > 1) = 1 -0.1408584

P(X > 1) = 0.8591416

P(X > 1) = 0.8591

( Round answer to specified number of decimal places)