Please do it by type not pic. 1. The Heart Association plans t install a free bl
ID: 358659 • Letter: P
Question
Please do it by type not pic.
1. The Heart Association plans t install a free blood pressure testing booth at the Palouse mall for a week. Previous experience indicates that, on average, 10 persons per hour request a test and the arrivals are Poisson distributed from an infinite population. Blood pressure measurements are exponential with an average time of 5 minutes per exam.
a. What is the average number of people in line?
b. What is the average number of people in the system?
c. What is the average amount of time a person can expect to spend in line?
d. What is the average amount of time it will take to measure a person's blood pressure, including waiting in line?
e. What is the probability of having 3 people in line ?
Explanation / Answer
Rate of request for blood pressure measurement = a =10 persons / hour
Rate of service of blood pressure measurement ( 5 minutes per exam ) = S = 60 /5 = 12 persons / hour
= a/ S x ( S – a ) hour
= 10 / 12 x ( 12 – 10 ) hour
= 10/24 hour
= 25 minutes
AVERAGE AMOUNT OF TIME A PERSON CAN EXPECT TO SPEND IN A LINE = 25 MINUTES
= a/ S x ( S – a ) + 1/S hour
= 10/24 + 1/12 hour
= 10/24 + 2/24 hour
= 12/24 hour
= 30 minutes
AVERAGE MOUNT OF TIME IT WILL TAKE TO MEASURE A PERSON’S BLOOD PRESSURE INCLUDING WAITING IN LINE= 30 MINUTES
= ( a/s)^3 x ( 1 – a/s )
= ( 10/12)^3 x ( 1 – 10/12)
= (10/12)^3 x 2/12
= 2000/20736
= 0.0964
PROBABILITY OF HAVING 3 PEOPLE IN LINE = 0.0964
PROBABILITY OF HAVING 3 PEOPLE IN LINE = 0.0964