Question

In: Statistics and Probability

The number of arrivals per minute at a bank located in the central business district of...

The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200​ minutes, with the results shown in the table below. Complete​ (a) through​ (c) to the right.

Arrivals, Frequency

0 13

1 25

2 47

3 40

4 32

5 23

6 12

7 6

8 2

Compute the standard deviation.

What is the probability that there will be fewer than 2 arrivals in a given​ minute?

Solutions

Expert Solution

Relative Frequency gives the answer of probability part. Relative frequency is nothing but ratio of frequency of a class and total frequency (here total frequency is 200).

Let x denotes number of arrivals and f denotes the frequencies.

where, n is total frequency (200) i.e.

Sample Standard deviation :

(Answer)

■ Probability that there will be fewer than 2 arrivals in a given​ minute = Probability that there will be 0 arrivals in a given​ minute + Probability that there will be 1 arrivals in a given​ minute = 0.065 + 0.125 = 0.19 (Answer)


Related Solutions

The number of arrivals per minute at a bank located in the central business district of...
The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200​ minutes, with the results shown in the table below. Complete​ (a) through​ (c) to the right. Arrivals Frequency 0 13 1 24 2 48 3 44 4 30 5 20 6 12 7 6 8 3 a. Compute the expected number of arrivals per minute. μ= ​(Type an integer or decimal rounded to three...
A bank with a branch located in a commercial district of a city has the business...
A bank with a branch located in a commercial district of a city has the business objective of improving the process for serving customers during the noon-to-1 PM lunch period. To do so, the waiting time (defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of 15 customers is selected and the waiting times were...
A bank with a branch located in a commercial district of a city has the business...
A bank with a branch located in a commercial district of a city has the business objective of improving the process for serving customers during the noon-to-1 pm lunch period. To do so, the waiting time (defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of 15 customers is selected and the waiting times are...
A bank with a branch located in a commercial district of a city has the business...
A bank with a branch located in a commercial district of a city has the business objective of improving the process for serving customers during the noon-to-1 PM lunch period. To do so, the waiting time (defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of 15 customers is selected and the waiting times were...
A bank with a branch located in a commercial district of a city has the business...
A bank with a branch located in a commercial district of a city has the business objective of improving the process for serving customers during the noon-to-1 pm lunch period. To do so, the waiting time (defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of 15 customers is selected and the waiting times are...
A bank with a branch located in a commercial district of a city has the business...
A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1 P.M. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window. Data are collected from a random sample of 15 customers...
A bank branch located in a commercial district of a city has the business objective of...
A bank branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1 p.m. lunch period. To do so, the waiting time (defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. Another bank in the area is also concerned with the noon-to-1 PM lunch period....
In a waiting line situation, arrivals occur at a rate of 3 per minute, and the...
In a waiting line situation, arrivals occur at a rate of 3 per minute, and the service times average 12 seconds. Assume the Poisson and exponential distributions. a. What is λ?   What is μ? b. Find average number of units in the system. c. Find average time in the waiting line. d. Find probability that there is one person waiting. e. Find probability an arrival will have to wait.
Q5.In a waiting line situation, arrivals occur at a rate of 2 per minute, and the...
Q5.In a waiting line situation, arrivals occur at a rate of 2 per minute, and the service times average 18 seconds. Assume the Poisson and exponential distributions [Hint: convert service time 18 seconds to service rate].JosiahA a.   What is l? b.   What is µ? c.   Find probability of no units in the system. d.   Find average number of units in the system. e.   Find average time in the waiting line. f.    Find average time in the system. g.   Find probability...
A bank with branches located in a commercial district of a city and in a residential...
A bank with branches located in a commercial district of a city and in a residential area has the business objective of developing an improved process for serving customers during the​ noon-to-1 P.M. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window. Data are collected from a random...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT