Suppose that you and two friends go to a​ restaurant, which last month filled approximately 90.5% of the orders correctly. Can you please complete part (d) below.   a.What is the probability that all three orders will be filled​ correctly?   b. What is the probability that none of the three orders will be filled​ correctly?   c. What is the probability that at least two of the three will be filled​ correctly? d. What are the mean and standard deviation of the binomial distribution used in​ (a) through​ (c)? Interpret these values.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

Question:

Suppose that you and two friends go to a​ restaurant, which last month filled approximately 90.5% of the orders correctly. Can you please complete part (d) below.

 

a.What is the probability that all three orders will be filled​ correctly?

 

b. What is the probability that none of the three orders will be filled​ correctly?

 

c. What is the probability that at least two of the three will be filled​ correctly?

d. What are the mean and standard deviation of the binomial distribution used in​ (a) through​ (c)? Interpret these values.

Answer: 
 
Part a

“Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question andmention the sub-parts to be solved.”.

Obtain the probability that all three orders will be filled correctly.

The probability that all three orders will be filled correctly is obtained below:

 

Use Excel to obtain the probability value for x equals 3.

Follow the instruction to obtain the P-value:

  1. Open EXCEL
  2. Go to Formula bar.
  3. In formula bar enter the function as“=BINOMDIST”
  4. Enter the number of success as 3.
  5. Enter the Trails as 3.
  6. Enter the probability as 0.905.
  7. Enter the cumulative as False.
  8. Click enter.

EXCEL output:

From the Excel output, the P-value is 0.7412.

 

Thus, the probability that all three orders will be filled correctly is 0.7412.

 

 

Part b

Obtain the probability that none of the all three orders will be filled correctly.

 

The probability that none of the all three orders will be filled correctly is obtained below:

 

Use Excel to obtain the probability value for x equals 0.

Follow the instruction to obtain the P-value:

  1. Open EXCEL
  2. Go to Formula bar.
  3. In formula bar enter the function as“=BINOMDIST”
  4. Enter the number of success as 0.
  5. Enter the Trails as 3.
  6. Enter the probability as 0.905.
  7. Enter the cumulative as False.
  8. Click enter.

EXCEL output:

From the Excel output, the P-value is 0.0009.

Thus, the probability that none of the all three orders will be filled correctly is 0.0009.

Part c

Obtain the probability that at least two of the three will be filled correctly.

The probability that at least two of the three will be filled correctly is obtained below:

 

 

Use Excel to obtain the probability value for x equals 1.

Follow the instruction to obtain the P-value:

  1. Open EXCEL
  2. Go to Formula bar.
  3. In formula bar enter the function as“=BINOMDIST”
  4. Enter the number of success as 1.
  5. Enter the Trails as 3.
  6. Enter the probability as 0.905.
  7. Enter the cumulative as True.
  8. Click enter.

EXCEL output:

From the Excel output, the P-value is 0.0254.

 

Thus, the probability that at least two of the three will be filled correctly is 0.9746

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman